Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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×#20259353 | C2 | semidirect |
| 3. #27133055 | C2 | semidirect |
| 4. #27133042 | C2 | semidirect |
| 5. #27133037 | C2 | semidirect |
| 6. C4×#15690271 | C2 | semidirect |
| 7. C2×C4⋊Q8×C191 | C2 | semidirect |
| 34. #15690271 | D4 | semidirect |
| 76. C4×C191 | #137 | semidirect |
| 83. C191 | #3152 | semidirect |
| 87. C2×C4⋊Q8 | D191 | semidirect |
| 161. C4 | #20259353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259353 | 2 |
| #27133213 | 2 |
| #27133055 | 2 |
| #27133042 | 2 |
| #27133037 | 2 |
| C4×#15690271 | 2 |
| C2×C4⋊Q8×C191 | 2 |
| #3152 | 191 |