Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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×#19153814 | C2 | semidirect |
| 3. C2×#19153741 | C2 | semidirect |
| 4. C2×#19153740 | C2 | semidirect |
| 6. #26041033 | C2 | semidirect |
| 76. C2×Dic181 | SD16 | semidirect |
| 126. C181 | #2013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668437 | 2 |
| C2×#19153814 | 2 |
| C2×#19153741 | 2 |
| C2×#19153740 | 2 |
| #26041182 | 2 |
| #26041033 | 2 |
| C22×SD16×C181 | 2 |
| #2013 | 181 |