Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
178 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D19 |
| commutator, socle | C22×C19 | C2×C42 |
| Fitting | C19×#322 | C2 |
| prime radical | C22×D19 | C42 |
| cosocle | C42×C19 | C23 |
| hypercenter | #322 | D19 |
| hypocenter | C19 | #1454 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C42 ◁ #322 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11926266 | C2 | semidirect |
| 5. #11926265 | C2 | semidirect |
| 6. C8×C19⋊C8 | C2 | semidirect |
| 7. C19×#322 | C2 | semidirect |
| 66. #322 | D19 | semidirect |
| 85. C19 | #1454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11926595 | 2 |
| #11926266 | 2 |
| #11926265 | 2 |
| C8×C19⋊C8 | 2 |
| C19×#322 | 2 |
| #1454 | 19 |