Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. #27133213 | C2 | semidirect |
| 2. C2×#20259319 | C2 | semidirect |
| 3. #27133040 | C2 | semidirect |
| 4. #27133010 | C2 | semidirect |
| 5. #27132859 | C2 | semidirect |
| 6. #27132799 | C2 | semidirect |
| 7. #431×C191 | C2 | semidirect |
| 12. C2×D1528 | C22 | semidirect |
| 13. #20259322 | C22 | semidirect |
| 18. #20259319 | C22 | semidirect |
| 23. C4×D764 | C22 | semidirect |
| 24. #20259244 | C22 | semidirect |
| 26. C4⋊C8×C191 | C22 | semidirect |
| 28. C4×C8×C191 | C22 | semidirect |
| 80. C2×C4×C191 | D8 | semidirect |
| 112. C191 | #3205 | semidirect |
| 120. #431 | D191 | semidirect |
| 138. C4⋊C8 | C2×D191 | semidirect |
| 141. C4×C8 | C2×D191 | semidirect |
| 193. C2×C4 | D1528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133213 | 2 |
| C2×#20259319 | 2 |
| #27133040 | 2 |
| #27133010 | 2 |
| #27132859 | 2 |
| #27132799 | 2 |
| #431×C191 | 2 |
| #3205 | 191 |