Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
940 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72259639 | C2 | semidirect |
| 2. C22×C4×#3861 | C2 | semidirect |
| 3. #72214952 | C2 | semidirect |
| 4. #72214657 | C2 | semidirect |
| 5. C4×#10596874 | C2 | semidirect |
| 6. C2×C4×#64424 | C2 | semidirect |
| 8. C4×C22⋊(C7⋊D7) | C3 | semidirect |
| 14. #11924217 | C4 | direct (N × H) |
| 19. C22×C4×C72 | C2×C3 | semidirect |
| 21. C2×C4×C7⋊D7 | C2×C3 | semidirect |
| 22. C22⋊(C7⋊Dic7) | C2×C3 | semidirect |
| 23. #11716070 | C2×C3 | semidirect |
| 24. #11716068 | C2×C3 | semidirect |
| 25. C4×C7⋊Dic7 | C2×C3 | semidirect |
| 29. C22×#3861 | C2×C4 | semidirect |
| 33. C2×#64424 | C2×C4 | semidirect |
| 35. C4×#3861 | D4 | semidirect |
| 38. #10596874 | C2×C4 | semidirect |
| 44. C22⋊(C7⋊D7) | C3×C4 | semidirect |
| 64. C22×C72 | C2×C3×C4 | semidirect |
| 68. C2×C7⋊D7 | C2×C3×C4 | semidirect |
| 70. C4×C72 | C3×D4 | semidirect |
| 73. C7⋊Dic7 | C2×C3×C4 | semidirect |
| 84. #3861 | C4×D4 | semidirect |
| 85. C22×C4×C7 | AGL(1,𝔽7) | semidirect |
| 120. C72 | C3×C4×D4 | semidirect |
| 136. C22×C7 | C4×AGL(1,𝔽7) | semidirect |
| 142. C4×C7 | (C22⋊D7)⋊C3 | semidirect |
| 159. C22×C4 | #64424 | semidirect |
| 191. C7 | C4×(C22⋊D7)⋊C3 | semidirect |
| 202. C22 | C4×#64424 | semidirect |
| 208. C4 | #11924217 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72259639 | 2 |
| C22×C4×#3861 | 2 |
| #72214952 | 2 |
| #72214657 | 2 |
| C4×#10596874 | 2 |
| C2×C4×#64424 | 2 |
| C2×#11924217 | 2 |
| C4×C22⋊(C7⋊D7) | 3 |
| C4×(C22⋊D7)⋊C3 | 7 |