Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27133042 | C2 | semidirect |
| 3. #27133013 | C2 | semidirect |
| 4. #27132870 | C2 | semidirect |
| 68. C2×C4×C191 | Q16 | semidirect |
| 92. C191 | #3209 | semidirect |
| 160. C2×C4 | #15690277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| #27133042 | 2 |
| #27133013 | 2 |
| #27132870 | 2 |
| #27132819 | 2 |
| #27132716 | 2 |
| C2×C4⋊Q8×C191 | 2 |
| #3209 | 191 |