Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1070 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1070 conjugacy classes of subgroups — too many to draw. Only its 150 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×C13 | C2×#99 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×Q8 | C23×C13 |
| prime radical | C2×C13×#532 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C13×#356 | C2 | semidirect |
| 3. C2×C13×#355 | C2 | semidirect |
| 4. C13×#1785 | C2 | semidirect |
| 63. #12701 | C13 | direct (N × H) |
| 125. C2×#356 | C2×C13 | semidirect |
| 126. C2×#355 | C2×C13 | semidirect |
| 127. #1785 | C2×C13 | semidirect |
| 323. C13 | #12701 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#532 | 2 |
| C2×C13×#356 | 2 |
| C2×C13×#355 | 2 |
| C13×#1785 | 2 |
| #12701 | 13 |