Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
262 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#19153741 | C2 | semidirect |
| 4. C2×#19153734 | C2 | semidirect |
| 6. #26041047 | C2 | semidirect |
| 7. C2×#108×C181 | C2 | semidirect |
| 109. C181 | #2052 | semidirect |
| 112. C2×#108 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| #26041281 | 2 |
| C2×#19153741 | 2 |
| C2×#19153734 | 2 |
| #26041245 | 2 |
| #26041047 | 2 |
| C2×#108×C181 | 2 |
| #2052 | 181 |