Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
592 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 70 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×C22⋊C4 | C23×C13 |
| prime radical | C13×#2670 | C2 |
| LCS | G ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#2029 | C2 | semidirect |
| 3. C13×#1602 | C2 | semidirect |
| 4. C13×#1596 | C2 | semidirect |
| 5. C13×#1351 | C2 | semidirect |
| 6. C13×#1343 | C2 | semidirect |
| 7. C13×#1316 | C2 | semidirect |
| 64. #12266 | C13 | direct (N × H) |
| 126. #2029 | C2×C13 | semidirect |
| 127. #1602 | C2×C13 | semidirect |
| 128. #1596 | C2×C13 | semidirect |
| 129. #1351 | C2×C13 | semidirect |
| 130. #1343 | C2×C13 | semidirect |
| 131. #1316 | C2×C13 | semidirect |
| 361. C13 | #12266 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2670 | 2 |
| C13×#2029 | 2 |
| C13×#1602 | 2 |
| C13×#1596 | 2 |
| C13×#1351 | 2 |
| C13×#1343 | 2 |
| C13×#1316 | 2 |
| #12266 | 13 |