Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D191 | C2 | semidirect |
| 4. #27132920 | C2 | semidirect |
| 5. #27132919 | C2 | semidirect |
| 6. #27132905 | C2 | semidirect |
| 7. #27132904 | C2 | semidirect |
| 8. #27132901 | C2 | semidirect |
| 9. #27132700 | C2 | semidirect |
| 10. #27132670 | C2 | semidirect |
| 11. #467×C191 | C2 | semidirect |
| 137. C191 | #3059 | semidirect |
| 147. #467 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D191 | 2 |
| C2×#20259328 | 2 |
| #27133236 | 2 |
| #27132920 | 2 |
| #27132919 | 2 |
| #27132905 | 2 |
| #27132904 | 2 |
| #27132901 | 2 |
| #27132700 | 2 |
| #27132670 | 2 |
| #467×C191 | 2 |
| #3059 | 191 |