Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
6046 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.
This group has 6046 conjugacy classes of subgroups — too many to draw. Only its 1539 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D7 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C24×C7×Q8 | C2 |
| socle, prime radical | C25×C7 | C23 |
| hypercenter | C24×Q8 | D7 |
| hypocenter | C7 | C22×#395 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C25 ◁ C24×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#90001 | C2 | direct (N × H) |
| 12. #90001 | C22 | direct (N × H) |
| 25. C23×Dic7 | Q8 | semidirect |
| 50. C22×Dic7 | C2×Q8 | semidirect |
| 79. C2×Dic7 | C22×Q8 | semidirect |
| 96. C22×C7 | #395 | semidirect |
| 125. C2×C7 | C2×#395 | semidirect |
| 146. C7 | C22×#395 | semidirect |
| 147. C22 | #90001 | direct (N × H) |
| 157. C2 | C2×#90001 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C7×Q8 | 2 |
| C23×Dic7⋊C4 | 2 |
| C2×#90001 | 2 |
| C22×C7⋊#95 | 2 |
| C22×#395 | 7 |