Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #29507727 | C2 | semidirect |
| 5. #29507622 | C2 | semidirect |
| 6. #29507478 | C2 | semidirect |
| 7. #343×C241 | C2 | semidirect |
| 11. #21440675 | C4 | semidirect |
| 37. C2×Dic482 | C2×C4 | semidirect |
| 61. M16×C241 | C2×C4 | semidirect |
| 124. C241 | #1882 | semidirect |
| 131. #343 | D241 | semidirect |
| 177. M16 | C4×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440675 | 2 |
| #29508198 | 2 |
| C2×#21440568 | 2 |
| #29507727 | 2 |
| #29507622 | 2 |
| #29507478 | 2 |
| #343×C241 | 2 |
| #1882 | 241 |