Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1854 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 331 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C23×C7 | C23×C4 |
| Fitting | C7×#1446 | C2 |
| socle, cosocle | C24×C7 | C24 |
| prime radical | C23×D28 | C22 |
| hypercenter | #1446 | D7 |
| hypocenter | C7 | #14662 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ #1446 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#89422 | C2 | semidirect |
| 3. C7×#1446 | C2 | semidirect |
| 4. #11729888 | C2 | semidirect |
| 5. #11727182 | C2 | semidirect |
| 10. C2×#6510 | C4 | semidirect |
| 53. #1446 | D7 | semidirect |
| 93. C4×Dic7 | C22⋊C4 | semidirect |
| 278. C7 | #14662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6510 | 2 |
| C2×#89422 | 2 |
| C7×#1446 | 2 |
| #11729888 | 2 |
| #11727182 | 2 |
| #11727180 | 2 |
| #14662 | 7 |