Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
214 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 92 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. #6599⋊C8 | C2 | semidirect |
| 3. #14272004 | C2 | semidirect |
| 4. C8×#6599 | C2 | semidirect |
| 40. #6599 | M16 | semidirect |
| 42. C8×C29 | M16 | semidirect |
| 44. #6597 | M16 | semidirect |
| 73. C29 | #1455 | semidirect |
| 101. C8 | #90800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90800 | 2 |
| #6599⋊C8 | 2 |
| #14272004 | 2 |
| C8×#6599 | 2 |
| M16×Dic29 | 2 |
| #1455 | 29 |