Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 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. C7×#3155 | C2 | semidirect |
| 2. #11741339 | C2 | semidirect |
| 3. C2×#89919 | C2 | semidirect |
| 4. #11729830 | C2 | semidirect |
| 5. #11729787 | C2 | semidirect |
| 6. #11727651 | C2 | semidirect |
| 7. #11725478 | C2 | semidirect |
| 62. C2×Dic28 | D4 | semidirect |
| 67. C2×D56 | D4 | semidirect |
| 83. #6386 | D4 | semidirect |
| 85. C2×C7⋊C16 | D4 | semidirect |
| 89. #3155 | D7 | semidirect |
| 407. C7 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3155 | 2 |
| #11741339 | 2 |
| C2×#89919 | 2 |
| #11729830 | 2 |
| #11729787 | 2 |
| #11727651 | 2 |
| #11725478 | 2 |
| #13334 | 7 |