Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#20259351 | C2 | semidirect |
| 2. C2×#20259346 | C2 | semidirect |
| 3. #27133211 | C2 | semidirect |
| 4. #124×D191 | C2 | semidirect |
| 5. #27133058 | C2 | semidirect |
| 6. #27133057 | C2 | semidirect |
| 7. #27133050 | C2 | semidirect |
| 8. #27133046 | C2 | semidirect |
| 9. #27133044 | C2 | semidirect |
| 10. #27132615 | C2 | semidirect |
| 11. #496×C191 | C2 | semidirect |
| 17. C2×Dic764 | C22 | semidirect |
| 18. C2×#15690277 | C22 | semidirect |
| 21. C2×#15690275 | C22 | semidirect |
| 24. #20259322 | C22 | semidirect |
| 28. #20259309 | C22 | semidirect |
| 34. #20259233 | C22 | semidirect |
| 35. C8×Dic191 | C22 | semidirect |
| 36. C2×SD16×C191 | C22 | semidirect |
| 38. #127×C191 | C22 | semidirect |
| 40. #97×C191 | C22 | semidirect |
| 62. #15690270 | D4 | semidirect |
| 134. C191 | #3153 | semidirect |
| 143. #496 | D191 | semidirect |
| 157. C2×SD16 | C2×D191 | semidirect |
| 162. #127 | C2×D191 | semidirect |
| 174. #97 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259351 | 2 |
| C2×#20259346 | 2 |
| #27133211 | 2 |
| #124×D191 | 2 |
| #27133058 | 2 |
| #27133057 | 2 |
| #27133050 | 2 |
| #27133046 | 2 |
| #27133044 | 2 |
| #27132615 | 2 |
| #496×C191 | 2 |
| #3153 | 191 |