Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
652 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 182 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. C2×Q8×#1181 | C2 | semidirect |
| 3. (C2×#1181)⋊Q8 | C2 | semidirect |
| 5. #14272113 | C2 | semidirect |
| 6. #14272107 | C2 | semidirect |
| 7. C22⋊C4×#1181 | C2 | semidirect |
| 8. C42×#1181 | C2 | semidirect |
| 25. C29×#124 | C4 | semidirect |
| 26. #11745309 | C4 | semidirect |
| 27. #11745298 | C4 | semidirect |
| 28. #11745247 | C4 | semidirect |
| 30. #11745237 | C4 | semidirect |
| 42. C2×Q8×C29 | C2×C4 | semidirect |
| 53. C2×Dic58 | C2×C4 | semidirect |
| 54. C2×Dic58 | C2×C4 | semidirect |
| 65. C22⋊C4×C29 | C2×C4 | semidirect |
| 66. C42×C29 | C2×C4 | semidirect |
| 67. C22⋊Dic29 | C2×C4 | semidirect |
| 68. #90781 | C2×C4 | semidirect |
| 69. #90781 | C2×C4 | semidirect |
| 70. C4×Dic29 | C2×C4 | semidirect |
| 71. C4×Dic29 | C2×C4 | semidirect |
| 126. #1181 | #124 | direct (N × H) |
| 156. #124 | #1181 | direct (N × H) |
| 173. C29 | C4×#124 | semidirect |
| 179. C2×Q8 | C2×#1181 | semidirect |
| 203. C22⋊C4 | C2×#1181 | semidirect |
| 211. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#1181 | 2 |
| C2×D4×#1181 | 2 |
| (C2×#1181)⋊Q8 | 2 |
| #14272115 | 2 |
| #14272113 | 2 |
| #14272107 | 2 |
| C22⋊C4×#1181 | 2 |
| C42×#1181 | 2 |
| #124×D29 | 2 |
| C4×#124 | 29 |