Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#20259355 | C2 | semidirect |
| 3. C22×#15690277 | C2 | semidirect |
| 4. #27133237 | C2 | semidirect |
| 5. #27133234 | C2 | semidirect |
| 6. #27133056 | C2 | semidirect |
| 7. #27133054 | C2 | semidirect |
| 8. #27133044 | C2 | semidirect |
| 9. #27133041 | C2 | semidirect |
| 10. #27132621 | C2 | semidirect |
| 11. C2×#137×C191 | C2 | semidirect |
| 143. C191 | #3156 | semidirect |
| 146. C2×#137 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259355 | 2 |
| C2×#20259342 | 2 |
| C22×#15690277 | 2 |
| #27133237 | 2 |
| #27133234 | 2 |
| #27133056 | 2 |
| #27133054 | 2 |
| #27133044 | 2 |
| #27133041 | 2 |
| #27132621 | 2 |
| C2×#137×C191 | 2 |
| #3156 | 191 |