Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
578 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19153731 | C2 | semidirect |
| 3. #26041134 | C2 | semidirect |
| 4. #26041046 | C2 | semidirect |
| 5. #518×C181 | C2 | semidirect |
| 9. #19153784 | C4 | semidirect |
| 25. C23×D181 | C2×C4 | semidirect |
| 33. C22⋊Dic181 | C2×C4 | semidirect |
| 44. C22×C4×C181 | D4 | semidirect |
| 71. C23×C181 | C22⋊C4 | semidirect |
| 84. C2×C4×C181 | C22⋊C4 | semidirect |
| 119. C181 | #1889 | semidirect |
| 122. #518 | D181 | semidirect |
| 158. C22×C4 | C22⋊D181 | semidirect |
| 186. C23 | #15668426 | semidirect |
| 204. C2×C4 | #15668426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153784 | 2 |
| C2×#19153731 | 2 |
| #26041134 | 2 |
| #26041046 | 2 |
| #518×C181 | 2 |
| #1889 | 181 |