Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
512 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 1. C22×Dic116 | C2 | semidirect |
| 3. #14271404 | C2 | direct (N × H) |
| 4. C2×#11745166 | C2 | semidirect |
| 5. C2×#11745164 | C2 | semidirect |
| 19. C2×Dic116 | C22 | semidirect |
| 20. #11745166 | C22 | semidirect |
| 21. #11745164 | C22 | semidirect |
| 47. C23×C29 | Q16 | semidirect |
| 74. C22×C29 | C2×Q16 | semidirect |
| 90. C2×C29 | #467 | semidirect |
| 109. C29 | C2×#467 | semidirect |
| 135. C23 | Dic116 | semidirect |
| 161. C22 | C2×Dic116 | semidirect |
| 171. C2 | #14271404 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic116 | 2 |
| C2×#11745286 | 2 |
| #14271404 | 2 |
| C2×#11745166 | 2 |
| C2×#11745164 | 2 |
| C23×C8×C29 | 2 |
| C2×#467 | 29 |