Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11739823 | C2 | semidirect |
| 2. #11739752 | C2 | semidirect |
| 3. #11736748 | C2 | semidirect |
| 4. C7×#1478 | C2 | semidirect |
| 5. #11728543 | C2 | semidirect |
| 6. #11728528 | C2 | semidirect |
| 7. #11725552 | C2 | semidirect |
| 65. #6437 | D4 | semidirect |
| 68. #6432 | D4 | semidirect |
| 70. C7×C4⋊C8 | D4 | semidirect |
| 80. C4⋊(C7⋊C8) | D4 | semidirect |
| 86. #1478 | D7 | semidirect |
| 95. C2×C7×D4 | D8 | semidirect |
| 274. C4⋊C8 | C22⋊D7 | semidirect |
| 343. C2×D4 | D56 | semidirect |
| 443. C7 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739823 | 2 |
| #11739752 | 2 |
| #11736748 | 2 |
| C7×#1478 | 2 |
| #11728543 | 2 |
| #11728528 | 2 |
| #11725552 | 2 |
| #10238 | 7 |