Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 4. #27132947 | C2 | semidirect |
| 5. #27132872 | C2 | semidirect |
| 8. #27132769 | C2 | semidirect |
| 9. #27132767 | C2 | semidirect |
| 127. C191 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133215 | 2 |
| C2×#20259287 | 2 |
| #27132993 | 2 |
| #27132947 | 2 |
| #27132872 | 2 |
| #27132821 | 2 |
| #27132818 | 2 |
| #27132769 | 2 |
| #27132767 | 2 |
| #27132717 | 2 |
| #483×C191 | 2 |
| #3113 | 191 |