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. #72228595 | C2 | semidirect |
| 2. #72214952 | C2 | semidirect |
| 3. C42×#3861 | C2 | semidirect |
| 4. C2×C4×#64424 | C2 | semidirect |
| 6. C4×C4⋊(C7⋊D7) | C3 | semidirect |
| 12. C4⋊#64424 | C4 | direct (N × H) |
| 15. C2×C4×C7⋊D7 | C2×C3 | semidirect |
| 16. C42×C72 | C2×C3 | semidirect |
| 17. #11716070 | C2×C3 | semidirect |
| 18. C4⋊(C7⋊Dic7) | C2×C3 | semidirect |
| 23. C2×#64424 | C2×C4 | semidirect |
| 25. C4×#3861 | C2×C4 | semidirect |
| 26. C4×#3861 | D4 | semidirect |
| 33. C4⋊(C7⋊D7) | C3×C4 | semidirect |
| 48. C2×C7⋊D7 | C2×C3×C4 | semidirect |
| 50. C4×C72 | C2×C3×C4 | semidirect |
| 51. C4×C72 | C3×D4 | semidirect |
| 60. #3861 | C4×D4 | semidirect |
| 63. C42×C7 | AGL(1,𝔽7) | semidirect |
| 86. C72 | C3×C4×D4 | semidirect |
| 102. C4×C7 | C4×AGL(1,𝔽7) | semidirect |
| 103. C4×C7 | C4⋊AGL(1,𝔽7) | semidirect |
| 117. C42 | #64424 | semidirect |
| 137. C7 | C4×C4⋊AGL(1,𝔽7) | semidirect |
| 148. C4 | C4×#64424 | semidirect |
| 149. C4 | C4⋊#64424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72228595 | 2 |
| #72214952 | 2 |
| C42×#3861 | 2 |
| C2×C4×#64424 | 2 |
| C2×C4⋊#64424 | 2 |
| C4×C4⋊(C7⋊D7) | 3 |
| C4×C4⋊AGL(1,𝔽7) | 7 |