Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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×#11745220 | C2 | semidirect |
| 3. C2×C4⋊#6599 | C2 | semidirect |
| 5. #14272029 | C2 | semidirect |
| 6. #14272029 | C2 | semidirect |
| 52. #90781 | C8 | semidirect |
| 73. C2×C4×C29 | C2×C8 | semidirect |
| 79. C2×Dic29 | C2×C8 | semidirect |
| 108. C2×D29 | C4⋊C8 | semidirect |
| 150. C29 | #1850 | semidirect |
| 214. C2×C4 | D29⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D29⋊C8 | 2 |
| C2×#11745220 | 2 |
| C2×C4⋊#6599 | 2 |
| C2×#11745219 | 2 |
| #14272029 | 2 |
| #14271010 | 2 |
| #1850 | 29 |