Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
290 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 290 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 | C2×D8×C149 | D4 |
| 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. #2254×C149 | C2 | semidirect |
| 4. #1674×C149 | C2 | semidirect |
| 5. #1365×C149 | C2 | semidirect |
| 6. Q8⋊C16×C149 | C2 | semidirect |
| 60. D8×C149 | Q16 | semidirect |
| 122. #12407 | C149 | direct (N × H) |
| 123. C149 | #12407 | direct (N × H) |
| 125. #2254 | C2×C149 | semidirect |
| 127. #1674 | C2×C149 | semidirect |
| 128. #1365 | C2×C149 | semidirect |
| 129. Q8⋊C16 | C2×C149 | semidirect |
| 183. D8 | Q16×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3380×C149 | 2 |
| #2254×C149 | 2 |
| #2224×C149 | 2 |
| #1674×C149 | 2 |
| #1365×C149 | 2 |
| Q8⋊C16×C149 | 2 |
| #1331×C149 | 2 |
| #12407 | 149 |