Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
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. #26041653 | C2 | semidirect |
| 3. #26041627 | C2 | semidirect |
| 4. #26041479 | C2 | semidirect |
| 5. #26041429 | C2 | semidirect |
| 6. #26041332 | C2 | semidirect |
| 7. #533×C181 | C2 | semidirect |
| 11. C2×#15668436 | C22 | semidirect |
| 16. C4⋊#13089678 | C22 | semidirect |
| 17. #19153736 | C22 | semidirect |
| 19. C4×#13089678 | C22 | semidirect |
| 20. C4⋊Q8×C181 | C22 | semidirect |
| 21. C4⋊Q8×C181 | C22 | semidirect |
| 26. C4×Q8×C181 | C22 | semidirect |
| 76. C2×C4×C181 | SD16 | semidirect |
| 104. C181 | #3208 | semidirect |
| 106. #533 | D181 | semidirect |
| 117. C4⋊Q8 | C2×D181 | semidirect |
| 118. C4⋊Q8 | C2×D181 | semidirect |
| 127. C4×Q8 | C2×D181 | semidirect |
| 180. C2×C4 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153813 | 2 |
| #26041653 | 2 |
| #26041627 | 2 |
| #26041479 | 2 |
| #26041429 | 2 |
| #26041332 | 2 |
| #533×C181 | 2 |
| #3208 | 181 |