Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27133429 | C2 | semidirect |
| 3. #27132679 | C2 | semidirect |
| 4. #27132668 | C2 | semidirect |
| 5. #27132435 | C2 | semidirect |
| 6. C191⋊#338 | C2 | semidirect |
| 7. C2×#100×C191 | C2 | semidirect |
| 11. C2×#15690275 | C4 | semidirect |
| 12. C2×#15690272 | C4 | semidirect |
| 112. C191 | #1903 | semidirect |
| 118. C2×#100 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259348 | 2 |
| #27133429 | 2 |
| #27132679 | 2 |
| #27132668 | 2 |
| #27132435 | 2 |
| C191⋊#338 | 2 |
| C2×#100×C191 | 2 |
| #1903 | 191 |