Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
872 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 214 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 |
|---|---|---|
| 1. C2×Q8×#10624382 | C2 | semidirect |
| 2. #26042231 | C2 | semidirect |
| 3. #26042221 | C2 | semidirect |
| 4. C4×C22⋊#10624382 | C2 | semidirect |
| 13. C2×#15668450 | C4 | semidirect |
| 14. C2×#15668449 | C4 | semidirect |
| 15. C2×#15668448 | C4 | semidirect |
| 20. C2×#41×C181 | C4 | semidirect |
| 51. C2×#10624382 | #41 | semidirect |
| 58. Dic362 | C22⋊C4 | semidirect |
| 69. Q8×C181 | C22⋊C4 | semidirect |
| 100. C181 | #2341 | semidirect |
| 111. C2×#41 | #10624382 | semidirect |
| 155. Q8 | C22⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10624382 | 2 |
| #26042231 | 2 |
| #26042221 | 2 |
| C4×C22⋊#10624382 | 2 |
| C2×#41×D181 | 2 |
| #2341 | 181 |