Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 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 | #383×C151 | C2 |
| prime radical | C22×D604 | C22 |
| hypercenter | #383 | D151 |
| hypocenter | C151 | #2852 |
| LCS | G ▷ C23×C151 ▷ C151 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#18012733 | C2 | semidirect |
| 2. C2×C42×D151 | C2 | semidirect |
| 3. #23752104 | C2 | semidirect |
| 4. #23752097 | C2 | semidirect |
| 6. #23752086 | C2 | semidirect |
| 7. #383×C151 | C2 | semidirect |
| 40. C42×C151 | D4 | semidirect |
| 71. C2×D151 | #126 | semidirect |
| 82. C151 | #2852 | semidirect |
| 90. #383 | D151 | semidirect |
| 123. C42 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012733 | 2 |
| C2×C42×D151 | 2 |
| #23752104 | 2 |
| #23752097 | 2 |
| #23752090 | 2 |
| #23752086 | 2 |
| #383×C151 | 2 |
| #2852 | 151 |