Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
604 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11733706 | C2 | semidirect |
| 2. C7×#2041 | C2 | semidirect |
| 4. #11729516 | C2 | semidirect |
| 5. #11725444 | C2 | semidirect |
| 6. #11725285 | C2 | semidirect |
| 7. #11725284 | C2 | semidirect |
| 70. #2041 | D7 | semidirect |
| 120. C7×C4⋊C4 | D8 | semidirect |
| 134. C4⋊Dic7 | D8 | semidirect |
| 356. C4⋊C4 | #1141 | semidirect |
| 435. C7 | #7738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11733706 | 2 |
| C7×#2041 | 2 |
| #11729521 | 2 |
| #11729516 | 2 |
| #11725444 | 2 |
| #11725285 | 2 |
| #11725284 | 2 |
| #7738 | 7 |