Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 3. #26041106 | C2 | semidirect |
| 4. #26041105 | C2 | semidirect |
| 5. #26041083 | C2 | semidirect |
| 7. #358×C181 | C2 | semidirect |
| 65. C181 | #2237 | semidirect |
| 72. #358 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041517 | 2 |
| #26041316 | 2 |
| #26041106 | 2 |
| #26041105 | 2 |
| #26041083 | 2 |
| #26041058 | 2 |
| #358×C181 | 2 |
| #2237 | 181 |