Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
668 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 181 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×#15668438 | C2 | semidirect |
| 2. C22×D1448 | C2 | semidirect |
| 3. C2×#19153813 | C2 | semidirect |
| 4. C2×#19153804 | C2 | semidirect |
| 5. #26041668 | C2 | direct (N × H) |
| 6. C2×#97×C181 | C2 | semidirect |
| 12. C2×#15668438 | C22 | semidirect |
| 14. C2×D1448 | C22 | semidirect |
| 16. #19153813 | C22 | semidirect |
| 18. #19153804 | C22 | semidirect |
| 22. #97×C181 | C22 | semidirect |
| 43. C2×C8×C181 | D4 | semidirect |
| 69. C8×C181 | C2×D4 | semidirect |
| 83. C2×C181 | #496 | semidirect |
| 88. C181 | C2×#496 | semidirect |
| 95. C2×#97 | D181 | semidirect |
| 111. #97 | C2×D181 | semidirect |
| 131. C2×C8 | D724 | semidirect |
| 158. C8 | C2×D724 | semidirect |
| 174. C2 | #26041668 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668438 | 2 |
| C22×D1448 | 2 |
| C2×#19153813 | 2 |
| C2×#19153804 | 2 |
| #26041668 | 2 |
| C2×#97×C181 | 2 |
| C2×#496 | 181 |