Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2127 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | #127 | C23×C13 |
| prime radical | C13×#535 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#535 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C13×#1412 | C2 | semidirect |
| 5. C13×#1409 | C2 | semidirect |
| 6. C13×#541 | C4 | semidirect |
| 8. C13×#497 | C4 | semidirect |
| 11. C13×#488 | C4 | semidirect |
| 16. C13×#433 | C4 | semidirect |
| 29. C13×C4⋊Q8 | C2×C4 | semidirect |
| 34. C13×#125 | C2×C4 | semidirect |
| 54. C13×#97 | C2×C4 | semidirect |
| 55. C4×C8×C13 | C2×C4 | semidirect |
| 56. #13610 | C13 | direct (N × H) |
| 99. #1412 | C2×C13 | semidirect |
| 100. #1409 | C2×C13 | semidirect |
| 133. #541 | C4×C13 | semidirect |
| 135. #497 | C4×C13 | semidirect |
| 138. #488 | C4×C13 | semidirect |
| 143. #433 | C4×C13 | semidirect |
| 176. C4⋊Q8 | C2×C4×C13 | semidirect |
| 181. #125 | C2×C4×C13 | semidirect |
| 201. #97 | C2×C4×C13 | semidirect |
| 202. C4×C8 | C2×C4×C13 | semidirect |
| 248. C13 | #13610 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3222 | 2 |
| C13×#2128 | 2 |
| C13×#2127 | 2 |
| C13×#1412 | 2 |
| C13×#1409 | 2 |
| #13610 | 13 |