Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
294 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C32×C4 | #106 |
| commutator | C8 | C2×C32×C16 |
| Frattini, cosocle | C82 | C22×C32 |
| socle, prime radical | C22×C32 | #334 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C4 ◁ C32×C4×C8 ◁ C32×C82 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#7099 | C3 | direct (N × H) |
| 17. #7099 | C32 | direct (N × H) |
| 30. C32×C16 | C16 | semidirect |
| 60. C3×C16 | C3×C16 | semidirect |
| 92. C16 | C32×C16 | semidirect |
| 98. C32 | #7099 | direct (N × H) |
| 115. C3 | C3×#7099 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1367 | 2 |
| C32×#1311 | 2 |
| C3×#7099 | 3 |