Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
120 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C19 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C23×C3×C19 |
| prime radical | C3×#41×C19 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C19 ◁ C2×C3×C4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×Q8×C19 | C2 | semidirect |
| 3. C3×Q16×C19 | C2 | semidirect |
| 4. C3×SD16×C19 | C2 | semidirect |
| 5. C3×M16×C19 | C2 | semidirect |
| 6. C19×#137 | C3 | direct (N × H) |
| 17. C2×Q8×C19 | C2×C3 | semidirect |
| 18. Q16×C19 | C2×C3 | semidirect |
| 19. SD16×C19 | C2×C3 | semidirect |
| 20. M16×C19 | C2×C3 | semidirect |
| 39. C3×#137 | C19 | direct (N × H) |
| 46. C3×C19 | #137 | direct (N × H) |
| 48. C2×C3×Q8 | C2×C19 | semidirect |
| 49. C3×Q16 | C2×C19 | semidirect |
| 50. C3×SD16 | C2×C19 | semidirect |
| 51. C3×M16 | C2×C19 | semidirect |
| 55. #137 | C3×C19 | direct (N × H) |
| 65. C19 | C3×#137 | direct (N × H) |
| 67. C2×Q8 | C2×C3×C19 | semidirect |
| 68. Q16 | C2×C3×C19 | semidirect |
| 69. SD16 | C2×C3×C19 | semidirect |
| 70. M16 | C2×C3×C19 | semidirect |
| 95. C3 | C19×#137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#41×C19 | 2 |
| C2×C3×Q8×C19 | 2 |
| C3×Q16×C19 | 2 |
| C3×SD16×C19 | 2 |
| C3×M16×C19 | 2 |
| C19×#137 | 3 |
| C3×#137 | 19 |