Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
442 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 118 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 | C2×#102 |
| commutator | C2×C8 | C22×C4×C149 |
| Frattini, cosocle | C22×C8 | C23×C149 |
| prime radical | C2×#466×C149 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C23×C4×C149 ◁ C23×C8×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2112×C149 | C2 | semidirect |
| 3. #1810×C149 | C2 | semidirect |
| 4. #1349×C149 | C2 | semidirect |
| 18. C22⋊C16×C149 | C22 | semidirect |
| 19. #341×C149 | C22 | semidirect |
| 150. #11895 | C149 | direct (N × H) |
| 151. C149 | #11895 | direct (N × H) |
| 153. #2112 | C2×C149 | semidirect |
| 154. #1810 | C2×C149 | semidirect |
| 155. #1349 | C2×C149 | semidirect |
| 169. C22⋊C16 | C22×C149 | semidirect |
| 170. #341 | C22×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#466×C149 | 2 |
| #2112×C149 | 2 |
| #1810×C149 | 2 |
| #1349×C149 | 2 |
| #11895 | 149 |