Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
696 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 290 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 |
|---|---|---|
| 2. C4⋊C4×#1181 | C2 | semidirect |
| 8. #11745345 | C4 | semidirect |
| 12. C2×C4⋊C4×C29 | C4 | semidirect |
| 13. C2×C4⋊Dic29 | C4 | semidirect |
| 14. C2×#90779 | C4 | semidirect |
| 15. C4⋊C4×D29 | C4 | semidirect |
| 31. C4⋊#1181 | C2×C4 | semidirect |
| 33. C4×#1181 | C2×C4 | semidirect |
| 47. C2×C4×C29 | C42 | semidirect |
| 51. C2×Dic29 | C42 | semidirect |
| 56. C4×D29 | C42 | semidirect |
| 94. C2×C4⋊C4 | #1181 | semidirect |
| 99. C29 | #2274 | semidirect |
| 138. C2×C4 | C4×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745345 | 2 |
| C4⋊C4×#1181 | 2 |
| C4×C22⋊#1181 | 2 |
| C2×C4⋊C4×D29 | 2 |
| #2274 | 29 |