Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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 |
|---|---|---|
| 1. C2×#19153903 | C2 | semidirect |
| 2. #26042314 | C2 | semidirect |
| 3. #26042310 | C2 | semidirect |
| 4. D4×#13089685 | C2 | semidirect |
| 5. D181⋊(C4⋊C8) | C2 | semidirect |
| 6. #26042253 | C2 | semidirect |
| 7. C4×#15668459 | C2 | semidirect |
| 32. #15668459 | D4 | semidirect |
| 92. C4×C181 | #131 | semidirect |
| 103. C181 | #2935 | semidirect |
| 201. C4 | #19153903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153903 | 2 |
| #26042314 | 2 |
| #26042310 | 2 |
| D4×#13089685 | 2 |
| D181⋊(C4⋊C8) | 2 |
| #26042253 | 2 |
| C4×#15668459 | 2 |
| #26041827 | 2 |
| #2935 | 181 |