Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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 |
|---|---|---|
| 3. #26041237 | C2 | semidirect |
| 4. #26041234 | C2 | semidirect |
| 5. M16×Dic181 | C2 | semidirect |
| 6. C2×#19153726 | C2 | semidirect |
| 8. #19153823 | C4 | semidirect |
| 21. #131×C181 | C4 | semidirect |
| 25. #15668433 | C2×C4 | semidirect |
| 26. C2×#13089678 | C2×C4 | semidirect |
| 39. M16×C181 | C2×C4 | semidirect |
| 40. C2×C8×C181 | C2×C4 | semidirect |
| 68. C181 | #2875 | semidirect |
| 79. #131 | Dic181 | semidirect |
| 100. M16 | C2×Dic181 | semidirect |
| 104. C2×C8 | C2×Dic181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153823 | 2 |
| #41×Dic181 | 2 |
| #26041237 | 2 |
| #26041234 | 2 |
| M16×Dic181 | 2 |
| C2×#19153726 | 2 |
| C2×#131×C181 | 2 |
| #2875 | 181 |