Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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×#90809 | C2 | semidirect |
| 3. #14271276 | C2 | semidirect |
| 4. #14271274 | C2 | semidirect |
| 5. #14271270 | C2 | semidirect |
| 6. #14271266 | C2 | semidirect |
| 7. #14271261 | C2 | semidirect |
| 8. #14271198 | C2 | semidirect |
| 9. #14271158 | C2 | semidirect |
| 10. #97×D29 | C2 | semidirect |
| 11. C29×#441 | C2 | semidirect |
| 17. #11745281 | C4 | semidirect |
| 42. #90809 | C2×C4 | semidirect |
| 50. Q16×C29 | C2×C4 | semidirect |
| 57. #90784 | C2×C4 | semidirect |
| 69. D232 | C2×C4 | semidirect |
| 71. C8×D29 | C2×C4 | semidirect |
| 116. #441 | D29 | semidirect |
| 154. C29 | #2943 | semidirect |
| 165. Q16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| C4×#90809 | 2 |
| #14271276 | 2 |
| #14271274 | 2 |
| #14271270 | 2 |
| #14271266 | 2 |
| #14271261 | 2 |
| #14271198 | 2 |
| #14271158 | 2 |
| #97×D29 | 2 |
| C29×#441 | 2 |
| #2943 | 29 |