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. C2×#20259319 | C2 | semidirect |
| 2. #27133039 | C2 | semidirect |
| 3. #27133011 | C2 | semidirect |
| 4. #27132858 | C2 | semidirect |
| 5. #27132796 | C2 | semidirect |
| 6. #27132716 | C2 | semidirect |
| 7. #532×C191 | C2 | semidirect |
| 11. C2×#15690272 | C22 | semidirect |
| 16. C4⋊(C191⋊C8) | C22 | semidirect |
| 17. #20259242 | C22 | semidirect |
| 19. C4×C191⋊C8 | C22 | semidirect |
| 21. C4⋊Q8×C191 | C22 | semidirect |
| 22. #127×C191 | C22 | semidirect |
| 27. C4×D4×C191 | C22 | semidirect |
| 81. C2×C4×C191 | D8 | semidirect |
| 112. C191 | #3205 | semidirect |
| 114. #532 | D191 | semidirect |
| 126. C4⋊Q8 | C2×D191 | semidirect |
| 131. #127 | C2×D191 | semidirect |
| 136. C4×D4 | C2×D191 | semidirect |
| 193. C2×C4 | #15690272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259319 | 2 |
| #27133039 | 2 |
| #27133011 | 2 |
| #27132858 | 2 |
| #27132796 | 2 |
| #27132716 | 2 |
| #532×C191 | 2 |
| #3205 | 191 |