Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
218 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 88 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×C19 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C4 | C23×C19 |
| prime radical | C19×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C19×#431 | C2 | semidirect |
| 3. C19×#383 | C2 | semidirect |
| 4. C19×#328 | C2 | semidirect |
| 7. C19×#125 | C4 | semidirect |
| 8. C19×#124 | C4 | semidirect |
| 12. C4×Q8×C19 | C4 | semidirect |
| 14. C4×D4×C19 | C4 | semidirect |
| 70. #1521 | C19 | direct (N × H) |
| 89. #431 | C2×C19 | semidirect |
| 90. #383 | C2×C19 | semidirect |
| 91. #328 | C2×C19 | semidirect |
| 99. #125 | C4×C19 | semidirect |
| 100. #124 | C4×C19 | semidirect |
| 104. C4×Q8 | C4×C19 | semidirect |
| 106. C4×D4 | C4×C19 | semidirect |
| 115. C19 | #1521 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#529 | 2 |
| C19×#431 | 2 |
| C19×#383 | 2 |
| C19×#328 | 2 |
| C19×#327 | 2 |
| #1521 | 19 |