Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D151 |
| commutator, socle, cosocle | C23×C151 | C24 |
| Fitting | #390×C151 | C2 |
| prime radical | C22×D4×C151 | C22 |
| hypercenter | #390 | D151 |
| hypocenter | C151 | #2808 |
| LCS | G ▷ C23×C151 ▷ C151 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23752137 | C2 | semidirect |
| 3. #23752124 | C2 | semidirect |
| 4. #23752118 | C2 | semidirect |
| 5. #23752110 | C2 | semidirect |
| 6. #23752105 | C2 | semidirect |
| 7. #23752105 | C2 | semidirect |
| 8. #23752093 | C2 | semidirect |
| 123. C151 | #2808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752137 | 2 |
| #23752126 | 2 |
| #23752124 | 2 |
| #23752118 | 2 |
| #23752110 | 2 |
| #23752105 | 2 |
| #23752093 | 2 |
| #390×C151 | 2 |
| #2808 | 151 |