Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
158 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C16 | C23 |
| commutator | C22 | C22×C7×C16 |
| Frattini, cosocle | C2×C16 | C23×C7 |
| socle, prime radical | C22×C7 | C22×C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #13660 | C7 | direct (N × H) |
| 25. C7×C32 | Q8 | semidirect |
| 71. C32 | C7×Q8 | semidirect |
| 104. C7 | #13660 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×C16 | 2 |
| C7×C4⋊C32 | 2 |
| C7×#1397 | 2 |
| C4×C7×C32 | 2 |
| #13660 | 7 |