Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3342 conjugacy classes of subgroups; only the 715 normal subgroups are shown.
This group has 3342 conjugacy classes of subgroups — too many to draw. Only its 715 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 | C22×C7×#127 | C2 |
| socle, cosocle | C24×C7 | C24 |
| hypercenter | C22×#127 | D7 |
| hypocenter | C7 | #14713 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C22×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#89993 | C2 | semidirect |
| 3. C2×#89707 | C2 | semidirect |
| 4. C2×C42×Dic7 | C2 | semidirect |
| 8. C2×C7×#127 | C4 | semidirect |
| 35. C2×C4×Dic7 | D4 | semidirect |
| 61. C42×C7 | C22⋊C4 | semidirect |
| 68. C2×#127 | Dic7 | semidirect |
| 98. C2×Dic7 | #127 | semidirect |
| 130. C4×C7 | #390 | semidirect |
| 157. C42 | C22⋊Dic7 | semidirect |
| 187. C7 | #14713 | semidirect |
| 202. C4 | #89993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#127 | 2 |
| C2×#89993 | 2 |
| C2×#89707 | 2 |
| C2×C42×Dic7 | 2 |
| #14713 | 7 |