Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
618 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 140 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 | C2×D4 |
| commutator | C2×C4 | C22×C4×C149 |
| Frattini, cosocle | C22×C4 | C23×C149 |
| socle | C22×C149 | C2×C22⋊C4 |
| prime radical | C22×#41×C149 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C149 ◁ C23×C4×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#104×C149 | C2 | semidirect |
| 3. #407×C149 | C2 | semidirect |
| 4. C4×C22⋊C4×C149 | C2 | semidirect |
| 8. C2×#41×C149 | C4 | semidirect |
| 10. C22×Q8×C149 | C4 | semidirect |
| 12. C22×D4×C149 | C4 | semidirect |
| 15. C2×M16×C149 | C22 | semidirect |
| 17. C2×C42×C149 | C22 | semidirect |
| 67. Q8×C149 | C22⋊C4 | semidirect |
| 72. D4×C149 | C22⋊C4 | semidirect |
| 103. C22×C149 | #104 | semidirect |
| 119. C149 | #1789 | direct (N × H) |
| 120. #1789 | C149 | direct (N × H) |
| 122. C2×#104 | C2×C149 | semidirect |
| 123. #407 | C2×C149 | semidirect |
| 124. C4×C22⋊C4 | C2×C149 | semidirect |
| 128. C2×#41 | C4×C149 | semidirect |
| 130. C22×Q8 | C4×C149 | semidirect |
| 132. C22×D4 | C4×C149 | semidirect |
| 135. C2×M16 | C22×C149 | semidirect |
| 137. C2×C42 | C22×C149 | semidirect |
| 187. Q8 | C22⋊C4×C149 | semidirect |
| 192. D4 | C22⋊C4×C149 | semidirect |
| 223. C22 | #104×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C149 | 2 |
| C2×#104×C149 | 2 |
| #407×C149 | 2 |
| C4×C22⋊C4×C149 | 2 |
| #1789 | 149 |