Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#20259321 | C2 | semidirect |
| 3. #27132957 | C2 | semidirect |
| 4. #27132952 | C2 | semidirect |
| 5. #27132947 | C2 | semidirect |
| 6. #27132942 | C2 | semidirect |
| 7. #27132706 | C2 | semidirect |
| 8. #27132686 | C2 | semidirect |
| 11. #428×C191 | C2 | semidirect |
| 44. #15690287 | Q8 | semidirect |
| 87. Dic382 | C2×Q8 | semidirect |
| 89. D764 | C2×Q8 | semidirect |
| 138. C191 | #3079 | semidirect |
| 147. #428 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259321 | 2 |
| #27133131 | 2 |
| #27132957 | 2 |
| #27132952 | 2 |
| #27132947 | 2 |
| #27132942 | 2 |
| #27132706 | 2 |
| #27132686 | 2 |
| #27132665 | 2 |
| #27132662 | 2 |
| #428×C191 | 2 |
| #3079 | 191 |