Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#20259232 | C2 | semidirect |
| 5. C2×C8×Dic191 | C2 | semidirect |
| 6. #27132418 | C2 | semidirect |
| 7. #336×C191 | C2 | semidirect |
| 16. (C2×D191)⋊C8 | C4 | semidirect |
| 17. (C2×D191)⋊C8 | C4 | semidirect |
| 104. C191 | #1750 | semidirect |
| 112. #336 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259279 | 2 |
| C2×(C2×D191)⋊C8 | 2 |
| C2×#20259232 | 2 |
| C2×C8×Dic191 | 2 |
| #27132418 | 2 |
| #336×C191 | 2 |
| #1750 | 191 |