Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11745281 | C2 | semidirect |
| 2. #14271714 | C2 | semidirect |
| 3. #14271548 | C2 | semidirect |
| 4. #14271540 | C2 | semidirect |
| 5. #14271537 | C2 | semidirect |
| 6. C4×C8×D29 | C2 | semidirect |
| 7. C29×#494 | C2 | semidirect |
| 41. C8×D29 | D4 | semidirect |
| 65. C4×C29 | #135 | semidirect |
| 72. #494 | D29 | semidirect |
| 95. C29 | #3147 | semidirect |
| 139. C4 | #11745281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| #14271714 | 2 |
| #14271548 | 2 |
| #14271540 | 2 |
| #14271537 | 2 |
| C4×C8×D29 | 2 |
| C29×#494 | 2 |
| #3147 | 29 |