Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #2206 |
| commutator, Frattini, cosocle | C2×C16 | C23×C149 |
| prime radical | #2263×C149 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C149 ◁ C2×C4×C149 ◁ C4×C8×C149 ◁ C4×C16×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2264×C149 | C2 | semidirect |
| 3. #2249×C149 | C2 | semidirect |
| 4. #2178×C149 | C2 | semidirect |
| 5. #1422×C149 | C2 | semidirect |
| 6. #1420×C149 | C2 | semidirect |
| 7. #1419×C149 | C2 | semidirect |
| 96. #13691 | C149 | direct (N × H) |
| 97. C149 | #13691 | direct (N × H) |
| 98. #2264 | C2×C149 | semidirect |
| 100. #2249 | C2×C149 | semidirect |
| 101. #2178 | C2×C149 | semidirect |
| 102. #1422 | C2×C149 | semidirect |
| 103. #1420 | C2×C149 | semidirect |
| 104. #1419 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2264×C149 | 2 |
| #2263×C149 | 2 |
| #2249×C149 | 2 |
| #2178×C149 | 2 |
| #1422×C149 | 2 |
| #1420×C149 | 2 |
| #1419×C149 | 2 |
| #13691 | 149 |