Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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. #14271241 | C2 | semidirect |
| 3. #14271240 | C2 | semidirect |
| 4. #14270913 | C2 | semidirect |
| 5. #14270892 | C2 | semidirect |
| 6. #14270885 | C2 | semidirect |
| 7. C29×D4⋊C8 | C2 | semidirect |
| 63. #6597 | M16 | semidirect |
| 84. D4⋊C8 | D29 | semidirect |
| 106. C29 | #1594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90782 | 2 |
| #14271241 | 2 |
| #14271240 | 2 |
| #14270913 | 2 |
| #14270892 | 2 |
| #14270885 | 2 |
| C29×D4⋊C8 | 2 |
| #1594 | 29 |