Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 536 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. #11741352 | C2 | semidirect |
| 3. C2×#89681 | C2 | semidirect |
| 4. C7×#2145 | C2 | semidirect |
| 5. #11728412 | C2 | semidirect |
| 6. #11728408 | C2 | semidirect |
| 7. #11725620 | C2 | semidirect |
| 90. #2145 | D7 | semidirect |
| 399. C7 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741352 | 2 |
| #11741339 | 2 |
| C2×#89681 | 2 |
| C7×#2145 | 2 |
| #11728412 | 2 |
| #11728408 | 2 |
| #11725620 | 2 |
| #13335 | 7 |