Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
412 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 2. #26041341 | C2 | direct (N × H) |
| 3. C2×#19153745 | C2 | semidirect |
| 5. C2×C4×#13089678 | C2 | semidirect |
| 6. C2×#97×C181 | C2 | semidirect |
| 14. #19153745 | C22 | semidirect |
| 16. C4×#13089678 | C22 | semidirect |
| 19. #97×C181 | C22 | semidirect |
| 66. C2×C181 | #433 | semidirect |
| 70. C181 | C2×#433 | semidirect |
| 76. C2×#97 | D181 | semidirect |
| 89. #97 | C2×D181 | semidirect |
| 138. C2 | #26041341 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153773 | 2 |
| #26041341 | 2 |
| C2×#19153745 | 2 |
| C2×#19153728 | 2 |
| C2×C4×#13089678 | 2 |
| C2×#97×C181 | 2 |
| C2×#433 | 181 |