Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19153744 | C2 | semidirect |
| 3. C4×#15668433 | C2 | semidirect |
| 4. C4×C4⋊C4×C181 | C2 | semidirect |
| 7. #19153816 | C4 | semidirect |
| 8. #19153813 | C4 | semidirect |
| 9. #19153804 | C4 | semidirect |
| 30. #15668433 | D4 | semidirect |
| 82. C4×C181 | #104 | semidirect |
| 92. C181 | #1980 | semidirect |
| 97. C4×C4⋊C4 | D181 | semidirect |
| 176. C4 | #19153744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| C2×#19153744 | 2 |
| C4×#15668433 | 2 |
| C4×C4⋊C4×C181 | 2 |
| #1980 | 181 |