Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
950 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 109 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×#3205 | C2 | semidirect |
| 2. #11740747 | C2 | semidirect |
| 3. #11740630 | C2 | semidirect |
| 4. #11729569 | C2 | semidirect |
| 5. #11729513 | C2 | semidirect |
| 6. #11728528 | C2 | semidirect |
| 7. #11725542 | C2 | semidirect |
| 39. C7×C4⋊Q8 | D4 | semidirect |
| 44. C7×#127 | D4 | semidirect |
| 64. C7×C4⋊C8 | D4 | semidirect |
| 73. C4⋊(C7⋊C8) | D4 | semidirect |
| 76. #3205 | D7 | semidirect |
| 133. C4×Dic7 | D8 | semidirect |
| 218. C4⋊Q8 | C22⋊D7 | semidirect |
| 231. #127 | C22⋊D7 | semidirect |
| 244. C4⋊C8 | C22⋊D7 | semidirect |
| 387. C7 | #10280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3205 | 2 |
| #11740747 | 2 |
| #11740630 | 2 |
| #11729569 | 2 |
| #11729513 | 2 |
| #11728528 | 2 |
| #11725542 | 2 |
| #10280 | 7 |