Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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. #27132563 | C2 | semidirect |
| 3. #27132555 | C2 | semidirect |
| 4. #27132546 | C2 | semidirect |
| 5. #27132541 | C2 | semidirect |
| 6. #27132539 | C2 | semidirect |
| 7. #27132537 | C2 | semidirect |
| 8. #27132523 | C2 | semidirect |
| 9. #381×C191 | C2 | semidirect |
| 13. #20259296 | C4 | semidirect |
| 37. C2×C22⋊D191 | C2×C4 | semidirect |
| 45. C4⋊Dic191 | C2×C4 | semidirect |
| 52. (C2×D191)⋊C4 | C2×C4 | semidirect |
| 56. C22×C4×C191 | C2×C4 | semidirect |
| 129. C191 | #2377 | semidirect |
| 138. #381 | D191 | semidirect |
| 176. C22×C4 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259296 | 2 |
| #27132563 | 2 |
| #27132555 | 2 |
| #27132546 | 2 |
| #27132541 | 2 |
| #27132539 | 2 |
| #27132537 | 2 |
| #27132523 | 2 |
| #381×C191 | 2 |
| #2377 | 191 |