Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
330 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #397 |
| 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 |
|---|---|---|
| 3. #1571×C149 | C2 | semidirect |
| 5. #1301×C149 | C2 | semidirect |
| 6. #1286×C149 | C2 | semidirect |
| 7. #1286×C149 | C2 | semidirect |
| 146. #10637 | C149 | direct (N × H) |
| 147. C149 | #10637 | direct (N × H) |
| 150. #1571 | C2×C149 | semidirect |
| 152. #1301 | C2×C149 | semidirect |
| 153. #1286 | C2×C149 | semidirect |
| 154. #1286 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1804×C149 | 2 |
| #1800×C149 | 2 |
| #1571×C149 | 2 |
| #1478×C149 | 2 |
| #1301×C149 | 2 |
| #1286×C149 | 2 |
| #10637 | 149 |