Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #27133041 | C2 | semidirect |
| 4. #27133012 | C2 | semidirect |
| 5. #27132872 | C2 | semidirect |
| 6. #27132871 | C2 | semidirect |
| 94. C2×Dic191 | Q16 | semidirect |
| 133. C191 | #3209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133215 | 2 |
| C2×#20259320 | 2 |
| #27133041 | 2 |
| #27133012 | 2 |
| #27132872 | 2 |
| #27132871 | 2 |
| #27132821 | 2 |
| #27132819 | 2 |
| #27132818 | 2 |
| #27132713 | 2 |
| #451×C191 | 2 |
| #3209 | 191 |