Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
534 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C149 |
| prime radical | C2×#127×C149 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3255×C149 | C2 | semidirect |
| 5. #1526×C149 | C2 | semidirect |
| 6. #1485×C149 | C2 | semidirect |
| 7. #1299×C149 | C2 | semidirect |
| 184. #10113 | C149 | direct (N × H) |
| 185. C149 | #10113 | direct (N × H) |
| 186. #3255 | C2×C149 | semidirect |
| 190. #1526 | C2×C149 | semidirect |
| 191. #1485 | C2×C149 | semidirect |
| 192. #1299 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3255×C149 | 2 |
| #3208×C149 | 2 |
| #3138×C149 | 2 |
| #1965×C149 | 2 |
| #1526×C149 | 2 |
| #1485×C149 | 2 |
| #1299×C149 | 2 |
| #10113 | 149 |