Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #26041636 | C2 | direct (N × H) |
| 3. C2×#19153739 | C2 | semidirect |
| 5. C2×C4×#13089678 | C2 | semidirect |
| 6. C2×#125×C181 | C2 | semidirect |
| 13. #19153739 | C22 | semidirect |
| 15. C4×#13089678 | C22 | semidirect |
| 17. #125×C181 | C22 | semidirect |
| 69. C2×C181 | #488 | semidirect |
| 73. C181 | C2×#488 | semidirect |
| 75. C2×#125 | D181 | semidirect |
| 85. #125 | C2×D181 | semidirect |
| 144. C2 | #26041636 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153804 | 2 |
| #26041636 | 2 |
| C2×#19153739 | 2 |
| C2×#19153736 | 2 |
| C2×C4×#13089678 | 2 |
| C2×#125×C181 | 2 |
| C2×#488 | 181 |