Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
252 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 77 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. #27132720 | C2 | semidirect |
| 2. #27132531 | C2 | semidirect |
| 3. #27132397 | C2 | semidirect |
| 12. C4⋊Q8×C191 | C4 | semidirect |
| 13. #127×C191 | C4 | semidirect |
| 18. C4×D4×C191 | C4 | semidirect |
| 82. C191 | #1514 | semidirect |
| 89. C4⋊Q8 | Dic191 | semidirect |
| 90. #127 | Dic191 | semidirect |
| 95. C4×D4 | Dic191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27132720 | 2 |
| #27132531 | 2 |
| #27132397 | 2 |
| #532×C191 | 2 |
| #1514 | 191 |