Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
882 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 239 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C23×D7 |
| commutator, socle | C23×C7 | C23×C4 |
| Fitting, prime radical | C7×#2397 | C2 |
| cosocle | C22×C4×C7 | C24 |
| hypercenter | #2397 | D7 |
| hypocenter | C7 | #23359 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C22×C4 ◁ #2397 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11729365 | C2 | semidirect |
| 3. #11729365 | C2 | semidirect |
| 4. #11729364 | C2 | semidirect |
| 5. #11727192 | C2 | semidirect |
| 228. C7 | #23359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2397 | 2 |
| #11729365 | 2 |
| #11729364 | 2 |
| #11727192 | 2 |
| #23359 | 7 |