Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11740633 | C2 | semidirect |
| 2. #11740611 | C2 | semidirect |
| 3. #11736500 | C2 | semidirect |
| 4. C7×#1545 | C2 | semidirect |
| 5. #11728543 | C2 | semidirect |
| 6. #11728511 | C2 | semidirect |
| 7. #11725521 | C2 | semidirect |
| 61. #6437 | D4 | semidirect |
| 68. #6432 | D4 | semidirect |
| 71. C7×C4⋊C8 | D4 | semidirect |
| 79. C4⋊(C7⋊C8) | D4 | semidirect |
| 84. #1545 | D7 | semidirect |
| 123. C2×D28 | D8 | semidirect |
| 274. C4⋊C8 | C22⋊D7 | semidirect |
| 443. C7 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740633 | 2 |
| #11740611 | 2 |
| #11736500 | 2 |
| C7×#1545 | 2 |
| #11728543 | 2 |
| #11728511 | 2 |
| #11725521 | 2 |
| #10238 | 7 |