Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
250 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C149 |
| prime radical | #550×C149 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C42×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #486×C149 | C2 | semidirect |
| 3. #474×C149 | C2 | semidirect |
| 4. #462×C149 | C2 | semidirect |
| 5. #331×C149 | C2 | semidirect |
| 6. Q8⋊C8×C149 | C2 | semidirect |
| 7. D4⋊C8×C149 | C2 | semidirect |
| 99. C149 | #1641 | direct (N × H) |
| 100. #1641 | C149 | direct (N × H) |
| 102. #486 | C2×C149 | semidirect |
| 103. #474 | C2×C149 | semidirect |
| 104. #462 | C2×C149 | semidirect |
| 105. #331 | C2×C149 | semidirect |
| 106. Q8⋊C8 | C2×C149 | semidirect |
| 107. D4⋊C8 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #550×C149 | 2 |
| #486×C149 | 2 |
| #474×C149 | 2 |
| #462×C149 | 2 |
| #331×C149 | 2 |
| Q8⋊C8×C149 | 2 |
| D4⋊C8×C149 | 2 |
| #1641 | 149 |