Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
360 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C149 |
| prime radical | #532×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 |
|---|---|---|
| 2. #1989×C149 | C2 | semidirect |
| 3. #1573×C149 | C2 | semidirect |
| 6. #1470×C149 | C2 | semidirect |
| 7. #1285×C149 | C2 | semidirect |
| 169. #10509 | C149 | direct (N × H) |
| 170. C149 | #10509 | direct (N × H) |
| 172. #1989 | C2×C149 | semidirect |
| 173. #1573 | C2×C149 | semidirect |
| 176. #1470 | C2×C149 | semidirect |
| 177. #1285 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3234×C149 | 2 |
| #1989×C149 | 2 |
| #1573×C149 | 2 |
| #1551×C149 | 2 |
| #1502×C149 | 2 |
| #1470×C149 | 2 |
| #1285×C149 | 2 |
| #10509 | 149 |