Finite Group DatabasebetaFinite Group DatabasebetaOrder 12393.
554 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C17 | C33 |
| commutator | C32 | C32×C9×C17 |
| Frattini, cosocle | C33 | C33×C17 |
| prime radical | C34×C17 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C17×C9⋊C9 | C3 | semidirect |
| 4. C17×#6855 | C3 | semidirect |
| 8. C32×C9×C17 | C9 | semidirect |
| 14. #10624548 | C17 | direct (N × H) |
| 32. C3×C9⋊C9 | C3×C17 | semidirect |
| 34. #6855 | C3×C17 | semidirect |
| 39. C32×C17 | C9⋊C9 | semidirect |
| 47. C9×C17 | C32⋊C9 | semidirect |
| 51. C32×C9 | C9×C17 | semidirect |
| 79. C17 | #10624548 | direct (N × H) |
| 84. C32 | C17×C9⋊C9 | semidirect |
| 92. C9 | C17×C32⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C9×C17 | 3 |
| C3×C17×C9⋊C9 | 3 |
| C3×C17×C32⋊C9 | 3 |
| C17×#6855 | 3 |
| #10624548 | 17 |