Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1246 conjugacy classes of subgroups; only the 406 normal subgroups are shown.
This group has 1246 conjugacy classes of subgroups — too many to draw. Only its 406 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C7 | C23 |
| commutator | C23 | C22×C7×C8 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle, prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #11380 | C7 | direct (N × H) |
| 12. C22×C7×Q8 | C8 | semidirect |
| 18. C22×C7×C8 | Q8 | semidirect |
| 73. C22×Q8 | C7×C8 | semidirect |
| 79. C22×C8 | C7×Q8 | semidirect |
| 140. C7 | #11380 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C7×Q8 | 2 |
| C2×C7×#336 | 2 |
| #11380 | 7 |