Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
698 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×C22⋊C4 | C23×C13 |
| prime radical | C13×#2404 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C22⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#1819 | C2 | semidirect |
| 3. C2×C13×#323 | C2 | semidirect |
| 4. C13×#1351 | C2 | semidirect |
| 5. C13×#1343 | C2 | semidirect |
| 6. C22×C13×#41 | C4 | semidirect |
| 10. C13×#393 | C4 | semidirect |
| 12. C13×#392 | C4 | semidirect |
| 17. C13×#381 | C4 | semidirect |
| 58. #11839 | C13 | direct (N × H) |
| 120. #1819 | C2×C13 | semidirect |
| 121. C2×#323 | C2×C13 | semidirect |
| 122. #1351 | C2×C13 | semidirect |
| 123. #1343 | C2×C13 | semidirect |
| 190. C22×#41 | C4×C13 | semidirect |
| 194. #393 | C4×C13 | semidirect |
| 196. #392 | C4×C13 | semidirect |
| 201. #381 | C4×C13 | semidirect |
| 352. C13 | #11839 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2404 | 2 |
| C13×#1819 | 2 |
| C2×C13×#323 | 2 |
| C13×#1351 | 2 |
| C13×#1343 | 2 |
| #11839 | 13 |