Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 94 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×#19153879 | C2 | semidirect |
| 2. C2×#19153878 | C2 | semidirect |
| 3. D181⋊(C22⋊C8) | C2 | semidirect |
| 4. #26042221 | C2 | semidirect |
| 14. C2×#15668450 | C4 | semidirect |
| 16. C2×#15668449 | C4 | semidirect |
| 18. C2×#15668448 | C4 | semidirect |
| 26. C2×#41×C181 | C4 | semidirect |
| 92. Dic362 | C22⋊C4 | semidirect |
| 95. D724 | C22⋊C4 | semidirect |
| 116. Q8×C181 | C22⋊C4 | semidirect |
| 119. D4×C181 | C22⋊C4 | semidirect |
| 164. C181 | #1788 | semidirect |
| 178. C2×#41 | #10624382 | semidirect |
| 257. Q8 | C22⋊#10624382 | semidirect |
| 266. D4 | C22⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153879 | 2 |
| C2×#19153878 | 2 |
| D181⋊(C22⋊C8) | 2 |
| #26042221 | 2 |
| C2×#41×D181 | 2 |
| #1788 | 181 |