Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27132716 | C2 | semidirect |
| 3. #27132396 | C2 | semidirect |
| 4. C4×C4⋊C4×C191 | C2 | semidirect |
| 6. #20259322 | C4 | semidirect |
| 7. #20259319 | C4 | semidirect |
| 12. C4×D764 | C4 | semidirect |
| 89. C191 | #1502 | semidirect |
| 93. C4×C4⋊C4 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133213 | 2 |
| #27132716 | 2 |
| #27132396 | 2 |
| C4×C4⋊C4×C191 | 2 |
| #1502 | 191 |