Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
458 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 458 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×C4⋊C4 | C23×C13 |
| prime radical | C13×#1598 | C2 |
| 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 |
|---|---|---|
| 1. C13×#2572 | C2 | semidirect |
| 2. C13×#2007 | C2 | semidirect |
| 3. C13×#1616 | C2 | semidirect |
| 5. C13×#1353 | C2 | semidirect |
| 6. C13×#1345 | C2 | semidirect |
| 7. C13×#1319 | C2 | semidirect |
| 65. #12195 | C13 | direct (N × H) |
| 116. #2572 | C2×C13 | semidirect |
| 117. #2007 | C2×C13 | semidirect |
| 118. #1616 | C2×C13 | semidirect |
| 120. #1353 | C2×C13 | semidirect |
| 121. #1345 | C2×C13 | semidirect |
| 122. #1319 | C2×C13 | semidirect |
| 313. C13 | #12195 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2572 | 2 |
| C13×#2007 | 2 |
| C13×#1616 | 2 |
| C13×#1598 | 2 |
| C13×#1353 | 2 |
| C13×#1345 | 2 |
| C13×#1319 | 2 |
| #12195 | 13 |