Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
476 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 3. #27132706 | C2 | semidirect |
| 4. #27132703 | C2 | semidirect |
| 5. #27132699 | C2 | semidirect |
| 6. C2×#20259253 | C2 | semidirect |
| 8. #20259329 | C4 | semidirect |
| 26. #15690271 | C2×C4 | semidirect |
| 27. C2×C191⋊C8 | C2×C4 | semidirect |
| 76. C191 | #2912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259329 | 2 |
| #27133146 | 2 |
| #27132706 | 2 |
| #27132703 | 2 |
| #27132699 | 2 |
| C2×#20259253 | 2 |
| #520×C191 | 2 |
| #2912 | 191 |