Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
696 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #392 |
| prime radical | C13×#2397 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#3101 | C2 | semidirect |
| 3. C13×#1995 | C2 | semidirect |
| 4. C13×#1486 | C2 | semidirect |
| 5. C13×#1274 | C2 | semidirect |
| 26. C13×C4⋊Q8 | D4 | semidirect |
| 49. C4×C8×C13 | D4 | semidirect |
| 51. #10015 | C13 | direct (N × H) |
| 83. C42×C13 | SD16 | semidirect |
| 87. #3101 | C2×C13 | semidirect |
| 89. #1995 | C2×C13 | semidirect |
| 90. #1486 | C2×C13 | semidirect |
| 91. #1274 | C2×C13 | semidirect |
| 157. C4⋊Q8 | D4×C13 | semidirect |
| 180. C4×C8 | D4×C13 | semidirect |
| 217. C42 | C13×SD16 | semidirect |
| 221. C13 | #10015 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3101 | 2 |
| C13×#2397 | 2 |
| C13×#1995 | 2 |
| C13×#1486 | 2 |
| C13×#1274 | 2 |
| #10015 | 13 |