Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
328 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 83 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. C7×#1574 | C2 | semidirect |
| 4. #11728507 | C2 | semidirect |
| 5. #11728502 | C2 | semidirect |
| 7. C7⋊#1309 | C2 | semidirect |
| 59. #1574 | D7 | semidirect |
| 268. C7 | #10612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1574 | 2 |
| #11728528 | 2 |
| #11728507 | 2 |
| #11728502 | 2 |
| #11728256 | 2 |
| C7⋊#1309 | 2 |
| #10612 | 7 |