Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
714 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 714 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 | C23×D4×C13 | C4 |
| LCS | G ▷ C24 ▷ C22 ▷ 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×#1462 | C2 | semidirect |
| 3. C13×#1317 | C2 | semidirect |
| 4. C13×#1316 | C2 | semidirect |
| 45. #11502 | C13 | direct (N × H) |
| 59. C24×C13 | M16 | semidirect |
| 84. C22×C4×C13 | M16 | semidirect |
| 97. #1462 | C2×C13 | semidirect |
| 98. #1317 | C2×C13 | semidirect |
| 99. #1316 | C2×C13 | semidirect |
| 254. C24 | C13×M16 | semidirect |
| 279. C22×C4 | C13×M16 | semidirect |
| 291. C13 | #11502 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2308 | 2 |
| C13×#1462 | 2 |
| C13×#1317 | 2 |
| C13×#1316 | 2 |
| #11502 | 13 |