Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
472 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C149 | #124 |
| commutator, Frattini, cosocle | C2×C42 | C23×C149 |
| socle | C22×C149 | #394 |
| prime radical | #3150×C149 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C149 ◁ C2×C42×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1940×C149 | C2 | semidirect |
| 3. #1540×C149 | C2 | semidirect |
| 4. #1502×C149 | C2 | semidirect |
| 5. #1275×C149 | C2 | semidirect |
| 149. #10546 | C149 | direct (N × H) |
| 150. C149 | #10546 | direct (N × H) |
| 152. #1940 | C2×C149 | semidirect |
| 153. #1540 | C2×C149 | semidirect |
| 154. #1502 | C2×C149 | semidirect |
| 155. #1275 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3150×C149 | 2 |
| #1940×C149 | 2 |
| #1540×C149 | 2 |
| #1502×C149 | 2 |
| #1275×C149 | 2 |
| #10546 | 149 |