Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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. #14272198 | C2 | semidirect |
| 2. #14272197 | C2 | semidirect |
| 3. #14272025 | C2 | semidirect |
| 4. #14272011 | C2 | semidirect |
| 5. D4⋊#6599 | C2 | semidirect |
| 6. #14272004 | C2 | semidirect |
| 63. #6597 | M16 | semidirect |
| 106. C29 | #1594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272198 | 2 |
| #14272197 | 2 |
| #14272025 | 2 |
| #14272011 | 2 |
| D4⋊#6599 | 2 |
| #14272004 | 2 |
| #14271243 | 2 |
| #1594 | 29 |