Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #27133071 | C2 | semidirect |
| 3. #27133069 | C2 | semidirect |
| 4. #27133067 | C2 | semidirect |
| 5. #27133065 | C2 | semidirect |
| 6. #27133064 | C2 | semidirect |
| 11. #500×C191 | C2 | semidirect |
| 42. #15690270 | Q8 | semidirect |
| 45. C8×D191 | Q8 | semidirect |
| 107. C191 | #3164 | semidirect |
| 113. #500 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133290 | 2 |
| #27133071 | 2 |
| #27133069 | 2 |
| #27133067 | 2 |
| #27133065 | 2 |
| #27133064 | 2 |
| #27132704 | 2 |
| #27132700 | 2 |
| #107×D191 | 2 |
| #27132617 | 2 |
| #500×C191 | 2 |
| #3164 | 191 |