Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14271835 | C2 | semidirect |
| 2. Q8×D116 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271444 | C2 | semidirect |
| 5. #14271359 | C2 | semidirect |
| 6. C4×D232 | C2 | semidirect |
| 7. C8×Q8×C29 | C2 | semidirect |
| 46. Q8×C29 | D8 | semidirect |
| 57. D116 | #41 | semidirect |
| 82. C8×Q8 | D29 | semidirect |
| 105. C29 | #3358 | semidirect |
| 129. Q8 | D232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271835 | 2 |
| Q8×D116 | 2 |
| #14271510 | 2 |
| #14271444 | 2 |
| #14271359 | 2 |
| C4×D232 | 2 |
| C8×Q8×C29 | 2 |
| #3358 | 29 |