Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14271885 | C2 | semidirect |
| 2. #14271556 | C2 | semidirect |
| 4. #14271385 | C2 | semidirect |
| 6. #14271372 | C2 | semidirect |
| 7. #14271293 | C2 | semidirect |
| 8. #14271262 | C2 | semidirect |
| 9. C4×Q16×C29 | C2 | semidirect |
| 107. C4×Q16 | D29 | semidirect |
| 137. C29 | #3402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271885 | 2 |
| #14271556 | 2 |
| #14271547 | 2 |
| #14271385 | 2 |
| #14271381 | 2 |
| #14271372 | 2 |
| #14271293 | 2 |
| #14271262 | 2 |
| C4×Q16×C29 | 2 |
| #3402 | 29 |