Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
392 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26041566 | C2 | semidirect |
| 3. #26041564 | C2 | semidirect |
| 4. #26041510 | C2 | semidirect |
| 5. #26041481 | C2 | semidirect |
| 6. #26041479 | C2 | semidirect |
| 7. C2×C4⋊#13089678 | C2 | semidirect |
| 8. #533×C181 | C2 | semidirect |
| 83. C2×C4×C181 | SD16 | semidirect |
| 112. C181 | #3246 | semidirect |
| 114. #533 | D181 | semidirect |
| 195. C2×C4 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041566 | 2 |
| #26041564 | 2 |
| #26041510 | 2 |
| #26041481 | 2 |
| #26041479 | 2 |
| C2×C4⋊#13089678 | 2 |
| #533×C181 | 2 |
| #3246 | 181 |