Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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×#19153762 | C2 | semidirect |
| 4. #26041084 | C2 | semidirect |
| 5. #26041083 | C2 | semidirect |
| 7. C2×Q32×C181 | C2 | semidirect |
| 70. C2×D181 | Q32 | semidirect |
| 82. C181 | #2188 | semidirect |
| 86. C2×Q32 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D181 | 2 |
| C2×#19153762 | 2 |
| #26041517 | 2 |
| #26041084 | 2 |
| #26041083 | 2 |
| #26041058 | 2 |
| C2×Q32×C181 | 2 |
| #2188 | 181 |