Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic58 | C2 | semidirect |
| 5. #14270911 | C2 | semidirect |
| 6. #14270895 | C2 | semidirect |
| 7. C29×Q8⋊C8 | C2 | semidirect |
| 52. Q8×C29 | SD16 | semidirect |
| 69. Dic58 | SD16 | semidirect |
| 94. Q8⋊C8 | D29 | semidirect |
| 116. C29 | #1623 | semidirect |
| 148. Q8 | #90773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic58 | 2 |
| #14271536 | 2 |
| #14271364 | 2 |
| #14271363 | 2 |
| #14270911 | 2 |
| #14270895 | 2 |
| C29×Q8⋊C8 | 2 |
| #1623 | 29 |