Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27133140 | C2 | semidirect |
| 5. C2×#20259240 | C2 | semidirect |
| 6. #27132419 | C2 | semidirect |
| 7. H(3,ℤ/4)×C191 | C2 | semidirect |
| 11. #20259322 | C4 | semidirect |
| 12. #20259310 | C4 | semidirect |
| 109. C191 | #1912 | semidirect |
| 117. H(3,ℤ/4) | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133239 | 2 |
| #27133140 | 2 |
| #27132681 | 2 |
| #27132679 | 2 |
| C2×#20259240 | 2 |
| #27132419 | 2 |
| H(3,ℤ/4)×C191 | 2 |
| #1912 | 191 |