Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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. #26041183 | C2 | semidirect |
| 3. #26041170 | C2 | semidirect |
| 4. #26041169 | C2 | semidirect |
| 6. #26041150 | C2 | semidirect |
| 7. #26041147 | C2 | semidirect |
| 8. C4×#15668426 | C2 | semidirect |
| 9. C4×C4⋊C4×C181 | C2 | semidirect |
| 13. #19153804 | C4 | semidirect |
| 34. C2×Dic362 | C2×C4 | semidirect |
| 47. #15668426 | C2×C4 | semidirect |
| 48. #15668426 | C2×C4 | semidirect |
| 58. C42×C181 | C2×C4 | semidirect |
| 118. C181 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D181 | semidirect |
| 177. C42 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153804 | 2 |
| #26041183 | 2 |
| #26041170 | 2 |
| #26041169 | 2 |
| #26041157 | 2 |
| #26041150 | 2 |
| #26041147 | 2 |
| C4×#15668426 | 2 |
| C4×C4⋊C4×C181 | 2 |
| #2337 | 181 |