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. #27133070 | C2 | semidirect |
| 3. #27133069 | C2 | semidirect |
| 4. #27133065 | C2 | semidirect |
| 5. #27133063 | C2 | semidirect |
| 6. #27133060 | C2 | semidirect |
| 11. #498×C191 | C2 | semidirect |
| 42. #15690270 | Q8 | semidirect |
| 45. C8×D191 | Q8 | semidirect |
| 99. C191 | #3163 | semidirect |
| 107. #498 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133290 | 2 |
| #27133070 | 2 |
| #27133069 | 2 |
| #27133065 | 2 |
| #27133063 | 2 |
| #27133060 | 2 |
| #27132702 | 2 |
| #27132698 | 2 |
| #106×D191 | 2 |
| #27132617 | 2 |
| #498×C191 | 2 |
| #3163 | 191 |