Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
322 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C13 |
| prime radical | C2×C13×D8 | D4 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ C8×Q8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#2241 | C2 | semidirect |
| 4. C13×#1670 | C2 | semidirect |
| 5. C13×#1364 | C2 | semidirect |
| 6. C13×Q8⋊C16 | C2 | semidirect |
| 53. #12356 | C13 | direct (N × H) |
| 87. #2241 | C2×C13 | semidirect |
| 89. #1670 | C2×C13 | semidirect |
| 90. #1364 | C2×C13 | semidirect |
| 91. Q8⋊C16 | C2×C13 | semidirect |
| 100. Q8×C13 | SD32 | semidirect |
| 214. C13 | #12356 | direct (N × H) |
| 222. Q8 | C13×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C13×D8 | 2 |
| C13×#2241 | 2 |
| C13×#2208 | 2 |
| C13×#1670 | 2 |
| C13×#1364 | 2 |
| C13×Q8⋊C16 | 2 |
| C13×#1331 | 2 |
| #12356 | 13 |