Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. #27132414 | C2 | semidirect |
| 5. #27132412 | C2 | semidirect |
| 6. #27132409 | C2 | semidirect |
| 7. #498×C191 | C2 | semidirect |
| 59. C8×C191 | SD16 | semidirect |
| 76. C191 | #1671 | semidirect |
| 78. #498 | D191 | semidirect |
| 136. C8 | #15690274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27132950 | 2 |
| #27132865 | 2 |
| C8×D764 | 2 |
| #27132414 | 2 |
| #27132412 | 2 |
| #27132409 | 2 |
| #498×C191 | 2 |
| #1671 | 191 |