Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1530 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1530 conjugacy classes of subgroups — too many to draw. Only its 371 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, cosocle | C24×C7 | C24 |
| prime radical | C24×D7 | C23 |
| hypercenter | C2×#384 | D7 |
| hypocenter | C7 | #14665 |
| 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 |
|---|---|---|
| 2. C2×C7×#384 | C2 | semidirect |
| 3. C2×#89709 | C2 | semidirect |
| 5. #11729320 | C2 | semidirect |
| 13. C2×#6439 | C4 | semidirect |
| 40. C2×#384 | D7 | semidirect |
| 67. C42×C7 | C22⋊C4 | semidirect |
| 173. C42 | (C2×D7)⋊C4 | semidirect |
| 208. C7 | #14665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6439 | 2 |
| C2×C7×#384 | 2 |
| C2×#89709 | 2 |
| #11729324 | 2 |
| #11729320 | 2 |
| #14665 | 7 |