Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 348 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 | C4×C13 | #410 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×M16 | C23×C13 |
| socle | C2×C13 | #1466 |
| prime radical | C13×#525 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C8×C13 ◁ C13×#405 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#2166 | C2 | semidirect |
| 3. C13×#1321 | C2 | semidirect |
| 4. C13×#1320 | C2 | semidirect |
| 41. #11537 | C13 | direct (N × H) |
| 77. #2166 | C2×C13 | semidirect |
| 78. #1321 | C2×C13 | semidirect |
| 79. #1320 | C2×C13 | semidirect |
| 198. C13 | #11537 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2929 | 2 |
| C13×#2166 | 2 |
| C13×#1321 | 2 |
| C13×#1320 | 2 |
| #11537 | 13 |