Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26041016 | C2 | direct (N × H) |
| 11. C22×Q8×C181 | C4 | semidirect |
| 15. C22⋊Q8×C181 | C4 | semidirect |
| 18. C2×C4⋊C4×C181 | C4 | semidirect |
| 29. C2×Q8×C181 | C2×C4 | semidirect |
| 42. C4⋊C4×C181 | C2×C4 | semidirect |
| 96. C2×C181 | #328 | semidirect |
| 100. C181 | C2×#328 | semidirect |
| 106. C22×Q8 | Dic181 | semidirect |
| 112. C22⋊Q8 | Dic181 | semidirect |
| 115. C2×C4⋊C4 | Dic181 | semidirect |
| 124. C2×Q8 | C2×Dic181 | semidirect |
| 143. C4⋊C4 | C2×Dic181 | semidirect |
| 197. C2 | #26041016 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13089678 | 2 |
| C2×#19153723 | 2 |
| #26041016 | 2 |
| C2×C22⋊Q8×C181 | 2 |
| C2×#328 | 181 |