Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 152 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. #14272114 | C2 | semidirect |
| 3. #14272112 | C2 | semidirect |
| 5. #14272109 | C2 | semidirect |
| 6. #14272108 | C2 | semidirect |
| 14. C29×#126 | C4 | semidirect |
| 15. #11745260 | C4 | semidirect |
| 18. #11745241 | C4 | semidirect |
| 19. #11745238 | C4 | semidirect |
| 38. C4⋊C4×C29 | C2×C4 | semidirect |
| 40. C42×C29 | C2×C4 | semidirect |
| 44. C4⋊Dic29 | C2×C4 | semidirect |
| 45. #90779 | C2×C4 | semidirect |
| 46. #90779 | C2×C4 | semidirect |
| 47. C4×Dic29 | C2×C4 | semidirect |
| 101. #126 | #1181 | semidirect |
| 114. C29 | #2383 | semidirect |
| 129. C4⋊C4 | C2×#1181 | semidirect |
| 137. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272114 | 2 |
| #14272113 | 2 |
| #14272112 | 2 |
| #14272110 | 2 |
| #14272109 | 2 |
| #14272108 | 2 |
| #126×D29 | 2 |
| #2383 | 29 |