Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #26041106 | C2 | semidirect |
| 5. #26041105 | C2 | semidirect |
| 6. #26041104 | C2 | semidirect |
| 7. #367×C181 | C2 | semidirect |
| 11. #19153755 | C4 | semidirect |
| 30. #15668424 | C2×C4 | semidirect |
| 34. C16×C181 | C2×C4 | semidirect |
| 63. C181 | #2159 | semidirect |
| 69. #367 | D181 | semidirect |
| 98. C16 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153755 | 2 |
| #26041316 | 2 |
| #107×D181 | 2 |
| #26041106 | 2 |
| #26041105 | 2 |
| #26041104 | 2 |
| #367×C181 | 2 |
| #2159 | 181 |