Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C149 | #2127 |
| commutator | C42 | C22×C4×C149 |
| Frattini, cosocle | #127 | C23×C149 |
| prime radical | #535×C149 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C149 ◁ C22×C149 ◁ C22×C4×C149 ◁ #535×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1412×C149 | C2 | semidirect |
| 5. #1409×C149 | C2 | semidirect |
| 6. #541×C149 | C4 | semidirect |
| 8. #497×C149 | C4 | semidirect |
| 11. #488×C149 | C4 | semidirect |
| 16. #433×C149 | C4 | semidirect |
| 29. C4⋊Q8×C149 | C2×C4 | semidirect |
| 34. #125×C149 | C2×C4 | semidirect |
| 54. #97×C149 | C2×C4 | semidirect |
| 55. C4×C8×C149 | C2×C4 | semidirect |
| 153. #13610 | C149 | direct (N × H) |
| 154. C149 | #13610 | direct (N × H) |
| 158. #1412 | C2×C149 | semidirect |
| 159. #1409 | C2×C149 | semidirect |
| 160. #541 | C4×C149 | semidirect |
| 162. #497 | C4×C149 | semidirect |
| 165. #488 | C4×C149 | semidirect |
| 170. #433 | C4×C149 | semidirect |
| 183. C4⋊Q8 | C2×C4×C149 | semidirect |
| 188. #125 | C2×C4×C149 | semidirect |
| 208. #97 | C2×C4×C149 | semidirect |
| 209. C4×C8 | C2×C4×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3222×C149 | 2 |
| #2128×C149 | 2 |
| #2127×C149 | 2 |
| #1412×C149 | 2 |
| #1409×C149 | 2 |
| #13610 | 149 |