Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
412 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 122 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 | C2×#102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C24×C7 | D8 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ C23×C7×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C7×#1348 | C2 | semidirect |
| 5. C22×C7×Q16 | C4 | semidirect |
| 11. C7×#467 | C4 | semidirect |
| 13. C2×C7×#107 | C4 | semidirect |
| 20. #11889 | C7 | direct (N × H) |
| 53. #1348 | C2×C7 | semidirect |
| 92. C22×Q16 | C4×C7 | semidirect |
| 98. #467 | C4×C7 | semidirect |
| 100. C2×#107 | C4×C7 | semidirect |
| 265. C7 | #11889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#467 | 2 |
| C7×#2112 | 2 |
| C7×#1807 | 2 |
| C7×#1348 | 2 |
| #11889 | 7 |