Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4390 conjugacy classes of subgroups; only the 651 normal subgroups are shown.
This group has 4390 conjugacy classes of subgroups — too many to draw. Only its 651 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, prime radical | C23×C7×#41 | C2 |
| socle, cosocle | C24×C7 | C24 |
| hypercenter | C23×#41 | D7 |
| hypocenter | C7 | #14337 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C23×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#89984 | C2 | semidirect |
| 3. #11729888 | C2 | semidirect |
| 4. #11729885 | C2 | semidirect |
| 6. C22×C7×#41 | C4 | semidirect |
| 52. C22×C4×C7 | C22⋊C4 | semidirect |
| 63. C22×#41 | Dic7 | semidirect |
| 146. C22×C4 | C22⋊Dic7 | semidirect |
| 183. C7 | #14337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×#41 | 2 |
| C2×#89984 | 2 |
| #11729888 | 2 |
| #11729885 | 2 |
| #14337 | 7 |