Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
848 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 104 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×#19153878 | C2 | semidirect |
| 2. D181⋊(C22⋊C8) | C2 | semidirect |
| 3. #26042221 | C2 | semidirect |
| 5. C2×D181⋊C8 | C22 | semidirect |
| 6. C2×C4⋊#10624382 | C22 | semidirect |
| 13. C22×D724 | C4 | semidirect |
| 18. C2×D4×D181 | C4 | semidirect |
| 21. C22×D4×C181 | C4 | semidirect |
| 83. D724 | C22⋊C4 | semidirect |
| 100. D4×C181 | C22⋊C4 | semidirect |
| 110. C22×C181 | #102 | semidirect |
| 123. C2×D181 | #102 | semidirect |
| 142. C181 | #1786 | semidirect |
| 156. C22×D4 | #10624382 | semidirect |
| 232. D4 | C22⋊#10624382 | semidirect |
| 269. C22 | #19153878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153878 | 2 |
| D181⋊(C22⋊C8) | 2 |
| #26042221 | 2 |
| C22×D4×D181 | 2 |
| #1786 | 181 |