Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27133141 | C2 | semidirect |
| 3. #27132672 | C2 | semidirect |
| 5. #27132434 | C2 | semidirect |
| 6. #27132420 | C2 | semidirect |
| 22. C2×Q16×C191 | C4 | semidirect |
| 23. C2×SD16×C191 | C4 | semidirect |
| 109. C191 | #1905 | semidirect |
| 122. C2×Q16 | Dic191 | semidirect |
| 123. C2×SD16 | Dic191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133141 | 2 |
| #27132680 | 2 |
| #27132672 | 2 |
| #27132637 | 2 |
| #27132434 | 2 |
| #27132420 | 2 |
| C2×#137×C191 | 2 |
| #1905 | 191 |