Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×D764 | C2 | semidirect |
| 2. #27133010 | C2 | semidirect |
| 3. #27132863 | C2 | semidirect |
| 5. #27132408 | C2 | semidirect |
| 6. #27132392 | C2 | semidirect |
| 7. Q8⋊C8×C191 | C2 | semidirect |
| 62. D764 | SD16 | semidirect |
| 70. Q8×C191 | D8 | semidirect |
| 99. C191 | #1627 | semidirect |
| 106. Q8⋊C8 | D191 | semidirect |
| 157. Q8 | D1528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D764 | 2 |
| #27133010 | 2 |
| #27132863 | 2 |
| #27132859 | 2 |
| #27132408 | 2 |
| #27132392 | 2 |
| Q8⋊C8×C191 | 2 |
| #1627 | 191 |