Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 290 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 |
|---|---|---|
| 4. C4⋊C4×Dic181 | C2 | semidirect |
| 5. #26041041 | C2 | semidirect |
| 6. #26041033 | C2 | semidirect |
| 7. C2×#107×C181 | C2 | semidirect |
| 15. #19153738 | C4 | semidirect |
| 118. C181 | #1925 | semidirect |
| 120. C2×#107 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153738 | 2 |
| C2×#19153736 | 2 |
| #26041180 | 2 |
| C4⋊C4×Dic181 | 2 |
| #26041041 | 2 |
| #26041033 | 2 |
| C2×#107×C181 | 2 |
| #1925 | 181 |