Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#15690274 | C2 | semidirect |
| 3. #27133141 | C2 | semidirect |
| 4. #27132887 | C2 | semidirect |
| 5. #27132861 | C2 | semidirect |
| 6. #27132691 | C2 | semidirect |
| 7. #27132669 | C2 | semidirect |
| 8. #27132659 | C2 | semidirect |
| 9. C2×#137×C191 | C2 | semidirect |
| 19. Q8×Dic191 | C22 | semidirect |
| 23. Dic191⋊C8 | C22 | semidirect |
| 24. #20259246 | C22 | semidirect |
| 26. #20259243 | C22 | semidirect |
| 30. C2×Q16×C191 | C22 | semidirect |
| 31. C2×SD16×C191 | C22 | semidirect |
| 55. C2×Q8×C191 | D4 | semidirect |
| 116. C191 | #3043 | semidirect |
| 118. C2×#137 | D191 | semidirect |
| 131. C2×Q16 | C2×D191 | semidirect |
| 134. C2×SD16 | C2×D191 | semidirect |
| 155. C2×Q8 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690274 | 2 |
| #27133227 | 2 |
| #27133141 | 2 |
| #27132887 | 2 |
| #27132861 | 2 |
| #27132691 | 2 |
| #27132669 | 2 |
| #27132659 | 2 |
| C2×#137×C191 | 2 |
| #3043 | 191 |