Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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×#2541 | C2 | semidirect |
| 2. #11740611 | C2 | semidirect |
| 3. #11739752 | C2 | semidirect |
| 4. #11729513 | C2 | semidirect |
| 5. #11729351 | C2 | semidirect |
| 6. #11727223 | C2 | semidirect |
| 7. #11725426 | C2 | semidirect |
| 65. #6437 | D4 | semidirect |
| 68. #6432 | D4 | semidirect |
| 77. C4⋊(C7⋊C8) | D4 | semidirect |
| 78. C4⋊(C7⋊C8) | D4 | semidirect |
| 83. #2541 | D7 | semidirect |
| 110. C2×C7×D4 | D8 | semidirect |
| 343. C2×D4 | #1141 | semidirect |
| 443. C7 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2541 | 2 |
| #11740611 | 2 |
| #11739752 | 2 |
| #11729513 | 2 |
| #11729351 | 2 |
| #11727223 | 2 |
| #11725426 | 2 |
| #10238 | 7 |