Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
6494 conjugacy classes of subgroups; only the 651 normal subgroups are shown.
This group has 6494 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 | C24×C7×D4 | C2 |
| socle, cosocle | C24×C7 | C24 |
| hypercenter | C24×D4 | D7 |
| hypocenter | C7 | #14335 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C24×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#90019 | C2 | semidirect |
| 3. C2×#89983 | C2 | semidirect |
| 4. #11729885 | C2 | semidirect |
| 8. C23×C7×D4 | C4 | semidirect |
| 12. C22×C22⋊Dic7 | C22 | semidirect |
| 15. C2×C7⋊#95 | C22 | semidirect |
| 55. C24×C7 | C22⋊C4 | semidirect |
| 69. C22×C4×C7 | C22⋊C4 | semidirect |
| 80. C23×D4 | Dic7 | semidirect |
| 172. C24 | C22⋊Dic7 | semidirect |
| 189. C22×C4 | C22⋊Dic7 | semidirect |
| 232. C7 | #14335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C7×D4 | 2 |
| C2×#90019 | 2 |
| C2×#89983 | 2 |
| #11729885 | 2 |
| #14335 | 7 |