Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×#19153885 | C2 | semidirect |
| 3. C2×#19153884 | C2 | semidirect |
| 5. #26042153 | C2 | semidirect |
| 6. #26042153 | C2 | semidirect |
| 23. C22⋊#13089678 | C4 | semidirect |
| 24. #19153728 | C4 | semidirect |
| 25. #19153728 | C4 | semidirect |
| 26. C22⋊C8×C181 | C4 | semidirect |
| 140. C181 | #1854 | semidirect |
| 166. C22⋊C8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153895 | 2 |
| C2×#19153885 | 2 |
| C2×#19153884 | 2 |
| #26042221 | 2 |
| #26042153 | 2 |
| C22⋊C8×D181 | 2 |
| #1854 | 181 |