Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2158 conjugacy classes of subgroups; only the 558 normal subgroups are shown.
This group has 2158 conjugacy classes of subgroups — too many to draw. Only its 558 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C23×C7×D4 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#399 | C2 | semidirect |
| 3. C2×C7×#384 | C2 | semidirect |
| 4. C4×C7×#95 | C2 | semidirect |
| 14. #15155 | C7 | direct (N × H) |
| 30. C7×#95 | D4 | semidirect |
| 31. C2×#399 | C2×C7 | semidirect |
| 33. C2×#384 | C2×C7 | semidirect |
| 34. C4×#95 | C2×C7 | semidirect |
| 105. #95 | C7×D4 | semidirect |
| 120. C4×C7 | #399 | semidirect |
| 173. C7 | #15155 | direct (N × H) |
| 188. C4 | C7×#399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#399 | 2 |
| C2×C7×#390 | 2 |
| C2×C7×#384 | 2 |
| C4×C7×#95 | 2 |
| #15155 | 7 |