Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
940 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 163 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. C4⋊C4×#3861 | C2 | semidirect |
| 2. #72214952 | C2 | semidirect |
| 3. C4×#10596874 | C2 | semidirect |
| 4. C2×C4×#64424 | C2 | semidirect |
| 6. #13096534 | C3 | semidirect |
| 12. C4⋊#64424 | C4 | semidirect |
| 15. C2×C4×C7⋊D7 | C2×C3 | semidirect |
| 16. C72×C4⋊C4 | C2×C3 | semidirect |
| 17. #11716070 | C2×C3 | semidirect |
| 18. C4×C7⋊Dic7 | C2×C3 | semidirect |
| 24. C2×#64424 | C2×C4 | semidirect |
| 26. C4×#3861 | C2×C4 | semidirect |
| 28. #10596874 | D4 | semidirect |
| 34. C4⋊(C7⋊D7) | C3×C4 | semidirect |
| 55. C2×C7⋊D7 | C2×C3×C4 | semidirect |
| 57. C4×C72 | C2×C3×C4 | semidirect |
| 59. C7⋊Dic7 | C3×D4 | semidirect |
| 74. #3861 | C4×D4 | semidirect |
| 79. C7×C4⋊C4 | AGL(1,𝔽7) | semidirect |
| 80. C7×C4⋊C4 | AGL(1,𝔽7) | semidirect |
| 120. C72 | C3×C4×D4 | semidirect |
| 145. C4×C7 | C4×AGL(1,𝔽7) | semidirect |
| 146. C4×C7 | C4×AGL(1,𝔽7) | semidirect |
| 162. C4⋊C4 | #64424 | semidirect |
| 188. C7 | #6456⋊C3 | semidirect |
| 189. C7 | #6456⋊C3 | semidirect |
| 201. C4 | C4×#64424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊C4×#3861 | 2 |
| #72214952 | 2 |
| C4×#10596874 | 2 |
| C2×C4×#64424 | 2 |
| C2×C4⋊#64424 | 2 |
| #13096534 | 3 |
| #6456⋊C3 | 7 |