Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
428 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 74 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×C4⋊C4 | C23×C13 |
| prime radical | C22×D4×C13 | D4 |
| LCS | G ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C4⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#2061 | C2 | semidirect |
| 3. C13×#1611 | C2 | semidirect |
| 5. C13×#1346 | C2 | semidirect |
| 7. C13×#1324 | C2 | semidirect |
| 64. #12248 | C13 | direct (N × H) |
| 110. C42×C13 | SD16 | semidirect |
| 112. #2061 | C2×C13 | semidirect |
| 113. #1611 | C2×C13 | semidirect |
| 115. #1346 | C2×C13 | semidirect |
| 117. #1324 | C2×C13 | semidirect |
| 289. C42 | C13×SD16 | semidirect |
| 290. C13 | #12248 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2609 | 2 |
| C13×#2061 | 2 |
| C13×#1611 | 2 |
| C13×#1599 | 2 |
| C13×#1346 | 2 |
| C13×#1345 | 2 |
| C13×#1324 | 2 |
| #12248 | 13 |