Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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. #27133037 | C2 | semidirect |
| 3. #27133011 | C2 | semidirect |
| 4. #27132863 | C2 | semidirect |
| 5. #27132813 | C2 | semidirect |
| 6. #27132716 | C2 | semidirect |
| 7. #533×C191 | C2 | semidirect |
| 11. C2×#15690274 | C22 | semidirect |
| 16. C4⋊(C191⋊C8) | C22 | semidirect |
| 17. #20259242 | C22 | semidirect |
| 19. C4×C191⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C191 | C22 | semidirect |
| 21. C4⋊Q8×C191 | C22 | semidirect |
| 26. C4×Q8×C191 | C22 | semidirect |
| 76. C2×C4×C191 | SD16 | semidirect |
| 104. C191 | #3208 | semidirect |
| 106. #533 | D191 | semidirect |
| 117. C4⋊Q8 | C2×D191 | semidirect |
| 118. C4⋊Q8 | C2×D191 | semidirect |
| 127. C4×Q8 | C2×D191 | semidirect |
| 180. C2×C4 | #15690274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259319 | 2 |
| #27133037 | 2 |
| #27133011 | 2 |
| #27132863 | 2 |
| #27132813 | 2 |
| #27132716 | 2 |
| #533×C191 | 2 |
| #3208 | 191 |