Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1330 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 158 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 | #379 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C13×#3484 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#1783 | C2 | semidirect |
| 3. C13×#1504 | C2 | semidirect |
| 4. C13×#1438 | C2 | semidirect |
| 5. C2×C13×H(5,𝔽2) | C4 | semidirect |
| 9. C13×#535 | C4 | semidirect |
| 13. C13×#518 | C4 | semidirect |
| 16. C13×#407 | C22 | semidirect |
| 17. C2×C13×#95 | C22 | semidirect |
| 57. #8453 | C13 | direct (N × H) |
| 69. C2×Q8×C13 | C22⋊C4 | semidirect |
| 87. C2×D4×C13 | C22⋊C4 | semidirect |
| 103. C13×C4⋊C4 | C22⋊C4 | semidirect |
| 112. #1783 | C2×C13 | semidirect |
| 113. #1504 | C2×C13 | semidirect |
| 114. #1438 | C2×C13 | semidirect |
| 167. C2×H(5,𝔽2) | C4×C13 | semidirect |
| 171. #535 | C4×C13 | semidirect |
| 175. #518 | C4×C13 | semidirect |
| 178. #407 | C22×C13 | semidirect |
| 179. C2×#95 | C22×C13 | semidirect |
| 266. C2×Q8 | C13×C22⋊C4 | semidirect |
| 284. C2×D4 | C13×C22⋊C4 | semidirect |
| 300. C4⋊C4 | C13×C22⋊C4 | semidirect |
| 308. C13 | #8453 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3484 | 2 |
| C13×#1783 | 2 |
| C13×#1504 | 2 |
| C13×#1438 | 2 |
| #8453 | 13 |