Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. C2×#19153778 | C2 | semidirect |
| 3. #26041361 | C2 | direct (N × H) |
| 4. C2×#19153736 | C2 | semidirect |
| 5. C2×C8×Dic181 | C2 | semidirect |
| 6. C2×#107×C181 | C2 | semidirect |
| 9. C2×D1448 | C4 | semidirect |
| 13. #19153778 | C22 | semidirect |
| 16. #19153736 | C22 | semidirect |
| 17. C8×Dic181 | C22 | semidirect |
| 20. #107×C181 | C22 | semidirect |
| 24. C2×D724 | C2×C4 | semidirect |
| 30. D1448 | C2×C4 | semidirect |
| 38. C2×C8×C181 | C2×C4 | semidirect |
| 48. D724 | C22×C4 | semidirect |
| 50. C2×Dic181 | D8 | semidirect |
| 62. C8×C181 | C22×C4 | semidirect |
| 76. Dic181 | C2×D8 | semidirect |
| 77. C2×C181 | C4×D8 | semidirect |
| 82. C181 | C2×C4×D8 | semidirect |
| 87. C2×#107 | D181 | semidirect |
| 101. #107 | C2×D181 | semidirect |
| 118. C2×C8 | C4×D181 | semidirect |
| 145. C8 | C2×C4×D181 | semidirect |
| 161. C2 | #26041361 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1448 | 2 |
| C2×#19153778 | 2 |
| #26041361 | 2 |
| C2×#19153736 | 2 |
| C2×C8×Dic181 | 2 |
| C2×#107×C181 | 2 |
| C2×C4×D8 | 181 |