Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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. #14272207 | C2 | semidirect |
| 2. #14272091 | C2 | semidirect |
| 3. #14272078 | C2 | semidirect |
| 4. C16×#1181 | C2 | semidirect |
| 12. C29×Q32 | C4 | semidirect |
| 13. #11745176 | C4 | semidirect |
| 14. D464 | C4 | semidirect |
| 57. Q32 | #1181 | semidirect |
| 65. C29 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272207 | 2 |
| #14272091 | 2 |
| #14272078 | 2 |
| C16×#1181 | 2 |
| #14271596 | 2 |
| #2178 | 29 |