Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
564 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 194 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. C22×#15668459 | C2 | semidirect |
| 2. C23×#13089685 | C2 | semidirect |
| 3. #26042308 | C2 | direct (N × H) |
| 4. C2×C4⋊#13089685 | C2 | semidirect |
| 5. C2×#19153873 | C2 | semidirect |
| 6. C2×C22⋊#13089685 | C2 | semidirect |
| 7. C2×#19153871 | C2 | semidirect |
| 10. C2×#15668459 | C22 | semidirect |
| 16. C22×#13089685 | C22 | semidirect |
| 17. C4⋊#13089685 | C22 | semidirect |
| 18. #19153873 | C22 | semidirect |
| 19. C22⋊#13089685 | C22 | semidirect |
| 20. #19153871 | C22 | semidirect |
| 35. C2×#13089685 | D4 | semidirect |
| 65. #13089685 | C2×D4 | semidirect |
| 87. C23×C181 | M16 | semidirect |
| 99. C22×C181 | C2×M16 | semidirect |
| 114. C2×C181 | #435 | semidirect |
| 119. C181 | C2×#435 | semidirect |
| 188. C23 | #15668459 | semidirect |
| 223. C22 | C2×#15668459 | semidirect |
| 235. C2 | #26042308 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668459 | 2 |
| C23×#13089685 | 2 |
| #26042308 | 2 |
| C2×C4⋊#13089685 | 2 |
| C2×#19153873 | 2 |
| C2×C22⋊#13089685 | 2 |
| C2×#19153871 | 2 |
| C2×#19153776 | 2 |
| C2×#435 | 181 |