Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19153808 | C2 | semidirect |
| 3. #26041648 | C2 | semidirect |
| 4. #26041644 | C2 | semidirect |
| 5. #26041634 | C2 | semidirect |
| 6. #26041281 | C2 | semidirect |
| 7. C4×M16×C181 | C2 | semidirect |
| 77. C181 | #3142 | semidirect |
| 85. C4×M16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| C2×#19153808 | 2 |
| #26041648 | 2 |
| #26041644 | 2 |
| #26041634 | 2 |
| #26041281 | 2 |
| C4×M16×C181 | 2 |
| #3142 | 181 |