Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C22×C7×D16 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2151 | C2 | semidirect |
| 3. C2×C7×#361 | C2 | semidirect |
| 4. C7×#1978 | C2 | semidirect |
| 5. C7×#1381 | C2 | semidirect |
| 17. #13439 | C7 | direct (N × H) |
| 41. #2151 | C2×C7 | semidirect |
| 42. C2×#361 | C2×C7 | semidirect |
| 43. #1978 | C2×C7 | semidirect |
| 44. #1381 | C2×C7 | semidirect |
| 183. C7 | #13439 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D16 | 2 |
| C7×#2151 | 2 |
| C2×C7×#361 | 2 |
| C7×#1978 | 2 |
| C7×#1381 | 2 |
| #13439 | 7 |