Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
416 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C149 | #353 |
| commutator | C42 | C22×C4×C149 |
| Frattini, cosocle | #127 | C23×C149 |
| socle | C2×C149 | C2×#353 |
| prime radical | #3147×C149 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C149 ◁ C2×C4×C149 ◁ C22×C4×C149 ◁ #532×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2126×C149 | C2 | semidirect |
| 3. #1409×C149 | C2 | semidirect |
| 4. #1408×C149 | C2 | semidirect |
| 6. #532×C149 | C4 | semidirect |
| 9. #494×C149 | C4 | semidirect |
| 11. #492×C149 | C4 | semidirect |
| 14. C2×C4×C8×C149 | C4 | semidirect |
| 124. #13583 | C149 | direct (N × H) |
| 125. C149 | #13583 | direct (N × H) |
| 127. #2126 | C2×C149 | semidirect |
| 128. #1409 | C2×C149 | semidirect |
| 129. #1408 | C2×C149 | semidirect |
| 131. #532 | C4×C149 | semidirect |
| 134. #494 | C4×C149 | semidirect |
| 136. #492 | C4×C149 | semidirect |
| 139. C2×C4×C8 | C4×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3147×C149 | 2 |
| #2126×C149 | 2 |
| #1409×C149 | 2 |
| #1408×C149 | 2 |
| #13583 | 149 |