Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
338 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 338 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 | C22×C149 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C149 |
| prime radical | #3391×C149 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C42×C149 ◁ C8×Q8×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2240×C149 | C2 | semidirect |
| 3. #2226×C149 | C2 | semidirect |
| 4. #1676×C149 | C2 | semidirect |
| 5. #1361×C149 | C2 | semidirect |
| 6. Q8⋊C16×C149 | C2 | semidirect |
| 7. #1331×C149 | C2 | semidirect |
| 135. #12384 | C149 | direct (N × H) |
| 136. C149 | #12384 | direct (N × H) |
| 138. #2240 | C2×C149 | semidirect |
| 139. #2226 | C2×C149 | semidirect |
| 140. #1676 | C2×C149 | semidirect |
| 141. #1361 | C2×C149 | semidirect |
| 142. Q8⋊C16 | C2×C149 | semidirect |
| 143. #1331 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3391×C149 | 2 |
| #2240×C149 | 2 |
| #2226×C149 | 2 |
| #1676×C149 | 2 |
| #1361×C149 | 2 |
| Q8⋊C16×C149 | 2 |
| #1331×C149 | 2 |
| #12384 | 149 |