Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 197 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, prime radical | C2×#120×C151 | C2 |
| hypercenter | C2×#120 | D151 |
| hypocenter | C151 | #2849 |
| LCS | G ▷ C23×C151 ▷ C151 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic151 | C2 | semidirect |
| 2. C2×#18012720 | C2 | semidirect |
| 3. #23752092 | C2 | semidirect |
| 4. #23752084 | C2 | semidirect |
| 5. #23752073 | C2 | semidirect |
| 6. #23752068 | C2 | semidirect |
| 13. C2×Dic151⋊C4 | C22 | semidirect |
| 16. C2×C22⋊Dic151 | C22 | semidirect |
| 17. C151⋊#95 | C22 | semidirect |
| 29. C22×Dic151 | D4 | semidirect |
| 87. C22×C151 | #123 | semidirect |
| 101. C151 | #2849 | semidirect |
| 189. C22 | #18012720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic151 | 2 |
| C2×#18012720 | 2 |
| #23752092 | 2 |
| #23752084 | 2 |
| #23752073 | 2 |
| #23752068 | 2 |
| C2×#120×C151 | 2 |
| #2849 | 151 |