Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
944 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C13×#2656 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#448 | C2 | semidirect |
| 3. C2×C13×#327 | C2 | semidirect |
| 4. C13×#1446 | C2 | semidirect |
| 5. C13×#1280 | C2 | semidirect |
| 24. C22×Q8×C13 | D4 | semidirect |
| 47. C13×C22⋊C8 | D4 | semidirect |
| 51. #9964 | C13 | direct (N × H) |
| 87. C22×C4×C13 | SD16 | semidirect |
| 101. C2×#448 | C2×C13 | semidirect |
| 103. C2×#327 | C2×C13 | semidirect |
| 104. #1446 | C2×C13 | semidirect |
| 105. #1280 | C2×C13 | semidirect |
| 197. C22×Q8 | D4×C13 | semidirect |
| 220. C22⋊C8 | D4×C13 | semidirect |
| 268. C22×C4 | C13×SD16 | semidirect |
| 282. C13 | #9964 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#448 | 2 |
| C13×#2656 | 2 |
| C2×C13×#327 | 2 |
| C13×#1446 | 2 |
| C13×#1280 | 2 |
| #9964 | 13 |