Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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. #14271067 | C2 | semidirect |
| 3. #14271054 | C2 | semidirect |
| 4. #14271053 | C2 | semidirect |
| 6. #14271034 | C2 | semidirect |
| 7. #14271031 | C2 | semidirect |
| 8. C4×#90781 | C2 | semidirect |
| 9. C4×C4⋊C4×C29 | C2 | semidirect |
| 24. #11745237 | C4 | semidirect |
| 47. C2×Dic58 | C2×C4 | semidirect |
| 51. C42×C29 | C2×C4 | semidirect |
| 55. #90781 | C2×C4 | semidirect |
| 56. #90781 | C2×C4 | semidirect |
| 120. C4×C4⋊C4 | D29 | semidirect |
| 150. C29 | #2337 | semidirect |
| 177. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745237 | 2 |
| #14271067 | 2 |
| #14271054 | 2 |
| #14271053 | 2 |
| #14271041 | 2 |
| #14271034 | 2 |
| #14271031 | 2 |
| C4×#90781 | 2 |
| C4×C4⋊C4×C29 | 2 |
| #2337 | 29 |