Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 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. #27133004 | C2 | semidirect |
| 3. #27132998 | C2 | semidirect |
| 4. #27132993 | C2 | semidirect |
| 5. #27132706 | C2 | semidirect |
| 6. #27132671 | C2 | semidirect |
| 18. #20259255 | C22 | semidirect |
| 19. #20259253 | C22 | semidirect |
| 20. #20259245 | C22 | semidirect |
| 21. #20259245 | C22 | semidirect |
| 116. C191 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259301 | 2 |
| #27133004 | 2 |
| #27132998 | 2 |
| #27132993 | 2 |
| #27132706 | 2 |
| #27132671 | 2 |
| #27132627 | 2 |
| C2×#117×C191 | 2 |
| #3095 | 191 |