Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
476 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 98 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 | C22×D4×C149 | D4 |
| 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. #3237×C149 | C2 | semidirect |
| 4. #1537×C149 | C2 | semidirect |
| 5. #1497×C149 | C2 | semidirect |
| 7. #1287×C149 | C2 | semidirect |
| 187. #10043 | C149 | direct (N × H) |
| 188. C149 | #10043 | direct (N × H) |
| 189. #3237 | C2×C149 | semidirect |
| 192. #1537 | C2×C149 | semidirect |
| 193. #1497 | C2×C149 | semidirect |
| 195. #1287 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3237×C149 | 2 |
| #3110×C149 | 2 |
| #3101×C149 | 2 |
| #1537×C149 | 2 |
| #1497×C149 | 2 |
| #1466×C149 | 2 |
| #1287×C149 | 2 |
| #10043 | 149 |