Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
470 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 110 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 | C24 | C22×C4×C13 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C13 |
| prime radical | C22×D4×C13 | C2×C4 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C13×#1326 | C2 | semidirect |
| 5. C13×#1317 | C2 | semidirect |
| 58. #11526 | C13 | direct (N × H) |
| 83. C22×C4×C13 | M16 | semidirect |
| 98. C13×C22⋊C4 | M16 | semidirect |
| 108. #1326 | C2×C13 | semidirect |
| 109. #1317 | C2×C13 | semidirect |
| 269. C22×C4 | C13×M16 | semidirect |
| 284. C22⋊C4 | C13×M16 | semidirect |
| 291. C13 | #11526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×#123 | 2 |
| C13×#1466 | 2 |
| C13×#1465 | 2 |
| C13×#1326 | 2 |
| C13×#1317 | 2 |
| #11526 | 13 |