Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3342 conjugacy classes of subgroups; only the 739 normal subgroups are shown.
This group has 3342 conjugacy classes of subgroups — too many to draw. Only its 739 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×C43×C7 | C2 |
| socle, cosocle | C24×C7 | C24 |
| prime radical | C22×#6437 | C2 |
| hypercenter | C2×C43 | D7 |
| hypocenter | C7 | #14713 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C43×C7 | C2 | semidirect |
| 3. C2×#89711 | C2 | semidirect |
| 4. C2×#89707 | C2 | semidirect |
| 12. C2×#6437 | C4 | semidirect |
| 31. C2×C42×C7 | D4 | semidirect |
| 39. C2×C43 | D7 | semidirect |
| 62. C42×C7 | C22⋊C4 | semidirect |
| 95. C2×C4×C7 | #127 | semidirect |
| 116. C2×C42 | D28 | semidirect |
| 131. C4×C7 | #390 | semidirect |
| 157. C42 | (C2×D7)⋊C4 | semidirect |
| 183. C2×C4 | #6437 | semidirect |
| 187. C7 | #14713 | semidirect |
| 202. C4 | #89711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6437 | 2 |
| C2×C43×C7 | 2 |
| C2×#89711 | 2 |
| C2×#89707 | 2 |
| #14713 | 7 |