Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
432 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 130 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×#99 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C22×Q8 | C23×C7 |
| prime radical | C23×C7 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. #12804 | C7 | direct (N × H) |
| 239. C7 | #12804 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2327 | 2 |
| C2×C7×#356 | 2 |
| C7×#1801 | 2 |
| C7×#1394 | 2 |
| #12804 | 7 |