Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27133042 | C2 | semidirect |
| 3. #27133011 | C2 | semidirect |
| 4. #27133010 | C2 | semidirect |
| 5. #27133009 | C2 | semidirect |
| 6. C8×C191⋊C8 | C2 | semidirect |
| 7. #486×C191 | C2 | semidirect |
| 74. C191 | #1709 | semidirect |
| 81. #486 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133042 | 2 |
| #27133039 | 2 |
| #27133011 | 2 |
| #27133010 | 2 |
| #27133009 | 2 |
| C8×C191⋊C8 | 2 |
| #486×C191 | 2 |
| #1709 | 191 |