Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #27133141 | C2 | semidirect |
| 3. #27132764 | C2 | semidirect |
| 4. SD16×Dic191 | C2 | semidirect |
| 5. #27132701 | C2 | semidirect |
| 6. #27132672 | C2 | semidirect |
| 8. #27132618 | C2 | semidirect |
| 12. Q8×Dic191 | C22 | semidirect |
| 20. #20259256 | C22 | semidirect |
| 21. #20259254 | C22 | semidirect |
| 22. #20259246 | C22 | semidirect |
| 24. #20259232 | C22 | semidirect |
| 25. C8×Dic191 | C22 | semidirect |
| 28. C2×SD16×C191 | C4 | semidirect |
| 50. C2×Q8×C191 | C2×C4 | semidirect |
| 58. SD16×C191 | C2×C4 | semidirect |
| 59. SD16×C191 | C2×C4 | semidirect |
| 60. C2×C8×C191 | C2×C4 | semidirect |
| 103. C191 | #2949 | semidirect |
| 116. C2×SD16 | Dic191 | semidirect |
| 139. C2×Q8 | C2×Dic191 | semidirect |
| 148. SD16 | C2×Dic191 | semidirect |
| 149. SD16 | C2×Dic191 | semidirect |
| 152. C2×C8 | C2×Dic191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133141 | 2 |
| #27133138 | 2 |
| #27132764 | 2 |
| SD16×Dic191 | 2 |
| #27132701 | 2 |
| #27132672 | 2 |
| #27132668 | 2 |
| #27132618 | 2 |
| C22×SD16×C191 | 2 |
| #2949 | 191 |