Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
624 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 624 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 | C4×C149 | B(4,𝔽2) |
| commutator | C2×Q8 | C22×C4×C149 |
| Frattini, cosocle | C2×#41 | C23×C149 |
| socle | C2×C149 | #1889 |
| prime radical | #3018×C149 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C149 ◁ C2×C4×C149 ◁ C2×#41×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2980×C149 | C2 | semidirect |
| 3. #2126×C149 | C2 | semidirect |
| 4. #1794×C149 | C2 | semidirect |
| 5. #1395×C149 | C2 | semidirect |
| 9. #456×C149 | C4 | semidirect |
| 11. #454×C149 | C4 | semidirect |
| 194. #13053 | C149 | direct (N × H) |
| 195. C149 | #13053 | direct (N × H) |
| 197. #2980 | C2×C149 | semidirect |
| 198. #2126 | C2×C149 | semidirect |
| 199. #1794 | C2×C149 | semidirect |
| 200. #1395 | C2×C149 | semidirect |
| 204. #456 | C4×C149 | semidirect |
| 206. #454 | C4×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3018×C149 | 2 |
| #2980×C149 | 2 |
| #2126×C149 | 2 |
| #1794×C149 | 2 |
| #1395×C149 | 2 |
| #13053 | 149 |