Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #27132976 | C2 | semidirect |
| 3. #27132958 | C2 | semidirect |
| 4. #27132863 | C2 | semidirect |
| 5. #27132802 | C2 | semidirect |
| 6. #27132761 | C2 | semidirect |
| 7. #27132720 | C2 | semidirect |
| 8. C2×C4×Q8×C191 | C2 | semidirect |
| 76. Q8×C191 | #41 | semidirect |
| 111. C191 | #3112 | semidirect |
| 114. C2×C4×Q8 | D191 | semidirect |
| 181. Q8 | #15690287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133213 | 2 |
| #27132976 | 2 |
| #27132958 | 2 |
| #27132863 | 2 |
| #27132802 | 2 |
| #27132761 | 2 |
| #27132720 | 2 |
| C2×C4×Q8×C191 | 2 |
| #3112 | 191 |