Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
364 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 170 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. #14272214 | C2 | semidirect |
| 2. #14272213 | C2 | semidirect |
| 3. #14272212 | C2 | semidirect |
| 4. Q8×#6599 | C2 | semidirect |
| 44. D29⋊C8 | Q8 | semidirect |
| 126. C29 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272214 | 2 |
| #14272213 | 2 |
| #14272212 | 2 |
| Q8×#6599 | 2 |
| #14272170 | 2 |
| #14272167 | 2 |
| #14272128 | 2 |
| C4×D29⋊C8 | 2 |
| #14271718 | 2 |
| #2960 | 29 |