Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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. C2×D4×Dic29 | C2 | semidirect |
| 3. C2×#11745255 | C2 | semidirect |
| 4. C2×#11745243 | C2 | semidirect |
| 5. #14271065 | C2 | semidirect |
| 6. #14271063 | C2 | semidirect |
| 7. #14271032 | C2 | semidirect |
| 8. C42×Dic29 | C2 | semidirect |
| 9. C29×#390 | C2 | semidirect |
| 19. #11745302 | C4 | semidirect |
| 35. C2×D4×C29 | C2×C4 | semidirect |
| 41. C2×C22⋊D29 | C2×C4 | semidirect |
| 50. C2×D116 | C2×C4 | semidirect |
| 62. C4×Dic29 | C2×C4 | semidirect |
| 63. C4×Dic29 | D4 | semidirect |
| 64. C4×Dic29 | D4 | semidirect |
| 116. C4×C29 | C4×D4 | semidirect |
| 119. Dic29 | C4×D4 | semidirect |
| 120. Dic29 | #127 | semidirect |
| 127. #390 | D29 | semidirect |
| 158. C29 | C4×#127 | semidirect |
| 169. C2×D4 | C4×D29 | semidirect |
| 247. C4 | #11745243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745302 | 2 |
| C2×D4×Dic29 | 2 |
| C2×#11745255 | 2 |
| C2×#11745243 | 2 |
| #14271065 | 2 |
| #14271063 | 2 |
| #14271032 | 2 |
| C42×Dic29 | 2 |
| C29×#390 | 2 |
| C4×#127 | 29 |