Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
At least 7995 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has at least 7995 conjugacy classes of subgroups — too many to draw. Only its 144 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. #72341955 | C2 | semidirect |
| 2. C2×#20612⋊C3 | C2 | semidirect |
| 3. #72341483 | C2 | semidirect |
| 5. #72249722 | C3 | semidirect |
| 6. C2×#87547 | C4 | semidirect |
| 9. C2×#1791⋊C3 | C22 | semidirect |
| 10. #20610⋊C3 | C22 | semidirect |
| 12. C2×#20612 | C2×C3 | semidirect |
| 13. #6370734 | C2×C3 | semidirect |
| 14. #392141 | C2×C3 | semidirect |
| 15. #87547 | C2×C4 | semidirect |
| 21. C2×H(7,𝔽2) | C3×C4 | semidirect |
| 24. C22×#418 | A4 | semidirect |
| 25. C2×#1791 | C22×C3 | semidirect |
| 26. #20610 | C22×C3 | semidirect |
| 39. C23×M16 | C2×A4 | semidirect |
| 40. C22×#117 | C2×A4 | semidirect |
| 41. C22×#102 | C2×A4 | semidirect |
| 51. C23×C8 | C22×A4 | semidirect |
| 52. C22×C4⋊C4 | C22×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72341955 | 2 |
| C2×#20612⋊C3 | 2 |
| #72341483 | 2 |
| C22×#87547 | 2 |
| #72249722 | 3 |
| A4×#418 | 4 |