Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1284 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 222 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C13 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×H(3,𝔽4) | C2 | semidirect |
| 2. C2×C13×#454 | C2 | semidirect |
| 3. C13×#2202 | C2 | direct (N × H) |
| 4. C2×C13×#355 | C2 | semidirect |
| 5. C2×C13×2−1+4 | C22 | semidirect |
| 8. C13×H(3,𝔽4) | C22 | semidirect |
| 13. C13×#454 | C22 | semidirect |
| 15. C2×C13×#101 | C22 | semidirect |
| 16. C13×#355 | C22 | semidirect |
| 20. C13×2−1+4 | C23 | semidirect |
| 45. C13×#101 | C23 | semidirect |
| 46. C2×#2202 | C13 | direct (N × H) |
| 88. C2×H(3,𝔽4) | C2×C13 | semidirect |
| 89. C2×#454 | C2×C13 | semidirect |
| 90. #2202 | C2×C13 | direct (N × H) |
| 91. C2×#355 | C2×C13 | semidirect |
| 124. C2×2−1+4 | C22×C13 | semidirect |
| 127. H(3,𝔽4) | C22×C13 | semidirect |
| 132. #454 | C22×C13 | semidirect |
| 134. C2×#101 | C22×C13 | semidirect |
| 135. #355 | C22×C13 | semidirect |
| 154. 2−1+4 | C23×C13 | semidirect |
| 179. #101 | C23×C13 | semidirect |
| 184. C2×C13 | #2202 | direct (N × H) |
| 227. C13 | C2×#2202 | direct (N × H) |
| 279. C2 | C13×#2202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×H(3,𝔽4) | 2 |
| C2×C13×#454 | 2 |
| C13×#2202 | 2 |
| C2×C13×#355 | 2 |
| C2×#2202 | 13 |