Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #391×C151 | C2 |
| prime radical | C22×D604 | C22 |
| hypercenter | #391 | D151 |
| hypocenter | C151 | #2804 |
| LCS | G ▷ C23×C151 ▷ C151 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23752154 | C2 | semidirect |
| 2. #23752125 | C2 | semidirect |
| 3. #23752123 | C2 | semidirect |
| 4. #23752118 | C2 | semidirect |
| 7. #23752086 | C2 | semidirect |
| 8. #23752083 | C2 | semidirect |
| 9. #391×C151 | C2 | semidirect |
| 37. C2×D604 | Q8 | semidirect |
| 128. C151 | #2804 | semidirect |
| 134. #391 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752154 | 2 |
| #23752125 | 2 |
| #23752123 | 2 |
| #23752118 | 2 |
| #23752114 | 2 |
| #23752090 | 2 |
| #23752086 | 2 |
| #23752083 | 2 |
| #391×C151 | 2 |
| #2804 | 151 |