Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#15668437 | C2 | semidirect |
| 2. #26041850 | C2 | semidirect |
| 3. #26041754 | C2 | semidirect |
| 4. #26041492 | C2 | semidirect |
| 5. #26041482 | C2 | semidirect |
| 6. #26041307 | C2 | semidirect |
| 7. #26041289 | C2 | semidirect |
| 8. #26041275 | C2 | semidirect |
| 14. #19153814 | C22 | semidirect |
| 15. #19153803 | C22 | semidirect |
| 23. #19153745 | C22 | semidirect |
| 24. #19153741 | C22 | semidirect |
| 25. #19153740 | C22 | semidirect |
| 26. #19153737 | C22 | semidirect |
| 116. C181 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668437 | 2 |
| #26041850 | 2 |
| #26041754 | 2 |
| #26041492 | 2 |
| #26041482 | 2 |
| #26041307 | 2 |
| #26041289 | 2 |
| #26041275 | 2 |
| C2×AGL(1,ℤ/8)×C181 | 2 |
| #3042 | 181 |