Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C2×#11745210 | C2 | semidirect |
| 3. C2×#11745209 | C2 | semidirect |
| 5. #14272037 | C2 | semidirect |
| 6. #14272037 | C2 | semidirect |
| 23. C29×C22⋊C8 | C4 | semidirect |
| 24. C22⋊#6597 | C4 | semidirect |
| 25. #11745168 | C4 | semidirect |
| 26. #11745168 | C4 | semidirect |
| 165. C22⋊C8 | #1181 | semidirect |
| 167. C29 | #1854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745345 | 2 |
| C2×#11745210 | 2 |
| C2×#11745209 | 2 |
| #14272105 | 2 |
| #14272037 | 2 |
| C22⋊C8×D29 | 2 |
| #1854 | 29 |