Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊(C3⋊#3771) | C2 | semidirect |
| 32. C34 | M32 | semidirect |
| 63. C33 | #812 | semidirect |
| 93. C32 | #63639 | semidirect |
| 94. C32 | #64218 | semidirect |
| 109. C3 | #11724242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#622 | 2 |
| C3⋊(C3⋊#3771) | 2 |
| #11724242 | 3 |
| #63639 | 9 |