Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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. #14271511 | C2 | semidirect |
| 2. #14271363 | C2 | semidirect |
| 4. #14270909 | C2 | semidirect |
| 5. Q8⋊#6597 | C2 | semidirect |
| 6. D4⋊#6597 | C2 | semidirect |
| 7. D4×Q8×C29 | C2 | semidirect |
| 57. Q8×C29 | D8 | semidirect |
| 59. D4×C29 | SD16 | semidirect |
| 95. D4×Q8 | D29 | semidirect |
| 124. C29 | #1627 | semidirect |
| 157. Q8 | #90782 | semidirect |
| 164. D4 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271511 | 2 |
| #14271363 | 2 |
| #14271358 | 2 |
| #14270909 | 2 |
| Q8⋊#6597 | 2 |
| D4⋊#6597 | 2 |
| D4×Q8×C29 | 2 |
| #1627 | 29 |