Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
272 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 74 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×D29⋊C16 | C2 | semidirect |
| 2. C2×#11745210 | C2 | semidirect |
| 3. #14272075 | C2 | direct (N × H) |
| 7. C2×D8×C29 | C4 | semidirect |
| 11. D8×D29 | C4 | semidirect |
| 13. C2×D232 | C4 | semidirect |
| 17. #11745210 | C22 | semidirect |
| 19. D29⋊C16 | C22 | semidirect |
| 33. D8×C29 | C2×C4 | semidirect |
| 39. D232 | C2×C4 | semidirect |
| 93. C2×C29 | #357 | semidirect |
| 96. D29 | #357 | semidirect |
| 106. C2×D8 | #1181 | semidirect |
| 114. C29 | C2×#357 | semidirect |
| 130. D8 | C2×#1181 | semidirect |
| 187. C2 | #14272075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D29⋊C16 | 2 |
| C2×#11745210 | 2 |
| #14272075 | 2 |
| C2×D8×D29 | 2 |
| C2×#357 | 29 |