Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
672 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #11727901 | C2 | semidirect |
| 5. #11727813 | C2 | semidirect |
| 6. #11725507 | C2 | semidirect |
| 7. #11725502 | C2 | semidirect |
| 10. C2×#6514 | C4 | semidirect |
| 12. C22×#1142 | C4 | semidirect |
| 23. #90005 | C4 | semidirect |
| 28. #89987 | C4 | semidirect |
| 45. C22×Dic14 | C2×C4 | semidirect |
| 63. #6489 | C2×C4 | semidirect |
| 66. C2×#1136 | C2×C4 | semidirect |
| 67. C22×C7⋊C8 | C2×C4 | semidirect |
| 467. C7 | #13100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741552 | 2 |
| #11741550 | 2 |
| C7×#1795 | 2 |
| #11727901 | 2 |
| #11727813 | 2 |
| #11725507 | 2 |
| #11725502 | 2 |
| #13100 | 7 |