Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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×#3414 | C2 | semidirect |
| 2. #11741373 | C2 | semidirect |
| 3. #11741361 | C2 | semidirect |
| 4. #11729834 | C2 | semidirect |
| 5. C2×#89361 | C2 | semidirect |
| 6. #11729191 | C2 | semidirect |
| 7. #11725622 | C2 | semidirect |
| 46. C2×C7×Q16 | D4 | semidirect |
| 50. C2×C7×D8 | D4 | semidirect |
| 77. C2×C7×C16 | D4 | semidirect |
| 83. #6393 | D4 | semidirect |
| 89. #3414 | D7 | semidirect |
| 250. C2×Q16 | C22⋊D7 | semidirect |
| 254. C2×D8 | C22⋊D7 | semidirect |
| 279. C2×C16 | C22⋊D7 | semidirect |
| 426. C7 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3414 | 2 |
| #11741373 | 2 |
| #11741361 | 2 |
| #11729834 | 2 |
| C2×#89361 | 2 |
| #11729191 | 2 |
| #11725622 | 2 |
| #13318 | 7 |