Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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 | #396×C151 | C2 |
| prime radical | C22×C22⋊D151 | C22 |
| hypercenter | #396 | D151 |
| hypocenter | C151 | #2801 |
| LCS | G ▷ C23×C151 ▷ C151 | |
| UCS | C1 ◁ C23 ◁ #396 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C151⋊#401 | C2 | semidirect |
| 2. #23752149 | C2 | semidirect |
| 4. #23752111 | C2 | semidirect |
| 5. #23752105 | C2 | semidirect |
| 6. #23752102 | C2 | semidirect |
| 7. #396×C151 | C2 | semidirect |
| 77. C151 | #2801 | semidirect |
| 81. #396 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C151⋊#401 | 2 |
| #23752149 | 2 |
| #23752128 | 2 |
| #23752111 | 2 |
| #23752105 | 2 |
| #23752102 | 2 |
| #396×C151 | 2 |
| #2801 | 151 |