Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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. #26041171 | C2 | semidirect |
| 4. #26041169 | C2 | semidirect |
| 6. #26041153 | C2 | semidirect |
| 7. #26041150 | C2 | semidirect |
| 8. #26041145 | C2 | semidirect |
| 9. #382×C181 | C2 | semidirect |
| 13. #19153804 | C4 | semidirect |
| 35. C2×Dic362 | C2×C4 | semidirect |
| 51. #15668426 | C2×C4 | semidirect |
| 52. #15668426 | C2×C4 | semidirect |
| 61. C42×C181 | C2×C4 | semidirect |
| 127. C181 | #2379 | semidirect |
| 137. #382 | D181 | semidirect |
| 189. 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 |
| #26041171 | 2 |
| #26041169 | 2 |
| #26041157 | 2 |
| #26041153 | 2 |
| #26041150 | 2 |
| #26041145 | 2 |
| #382×C181 | 2 |
| #2379 | 181 |