Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2286 conjugacy classes of subgroups; only the 947 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 947 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 | C2×C7×#384 | C2 |
| socle, prime radical, cosocle | C24×C7 | C24 |
| hypercenter | C2×#384 | D7 |
| hypocenter | C7 | #14692 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C42×Dic7 | C4 | semidirect |
| 48. C42×C7 | C4⋊C4 | semidirect |
| 51. C4×Dic7 | C4⋊C4 | semidirect |
| 101. C4×C7 | #384 | semidirect |
| 103. Dic7 | #384 | semidirect |
| 121. C42 | Dic7⋊C4 | semidirect |
| 144. C7 | #14692 | semidirect |
| 155. C4 | #89748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#384 | 2 |
| C2×#89748 | 2 |
| C2×#89707 | 2 |
| C2×C42×Dic7 | 2 |
| #14692 | 7 |