Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
500 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C149 |
| prime radical | #3214×C149 | C2 |
| 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. #3112×C149 | C2 | semidirect |
| 3. #3103×C149 | C2 | semidirect |
| 4. #1536×C149 | C2 | semidirect |
| 5. #1496×C149 | C2 | semidirect |
| 6. #1467×C149 | C2 | semidirect |
| 7. #1287×C149 | C2 | semidirect |
| 196. #10040 | C149 | direct (N × H) |
| 197. C149 | #10040 | direct (N × H) |
| 199. #3112 | C2×C149 | semidirect |
| 200. #3103 | C2×C149 | semidirect |
| 201. #1536 | C2×C149 | semidirect |
| 202. #1496 | C2×C149 | semidirect |
| 203. #1467 | C2×C149 | semidirect |
| 204. #1287 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3214×C149 | 2 |
| #3112×C149 | 2 |
| #3103×C149 | 2 |
| #1536×C149 | 2 |
| #1496×C149 | 2 |
| #1467×C149 | 2 |
| #1287×C149 | 2 |
| #10040 | 149 |