Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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×#19153824 | C2 | semidirect |
| 3. #26041356 | C2 | semidirect |
| 4. #26041344 | C2 | semidirect |
| 5. #26041247 | C2 | semidirect |
| 6. C2×C4×#13089678 | C2 | semidirect |
| 7. #423×C181 | C2 | semidirect |
| 34. C2×#13089678 | D4 | semidirect |
| 75. C4×C181 | #131 | semidirect |
| 83. C181 | #2931 | semidirect |
| 89. #423 | D181 | semidirect |
| 160. C4 | #19153824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153824 | 2 |
| #26041829 | 2 |
| #26041356 | 2 |
| #26041344 | 2 |
| #26041247 | 2 |
| C2×C4×#13089678 | 2 |
| #423×C181 | 2 |
| #2931 | 181 |