Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2080 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 2080 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C13×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#535 | C2 | semidirect |
| 2. C2×C13×#447 | C2 | semidirect |
| 3. C13×#1999 | C2 | semidirect |
| 4. C13×#1875 | C2 | semidirect |
| 5. C13×#1780 | C2 | semidirect |
| 7. C23×D4×C13 | C22 | semidirect |
| 13. C2×C13×#121 | C22 | semidirect |
| 16. C2×C13×#117 | C22 | semidirect |
| 18. C2×C13×#102 | C22 | semidirect |
| 19. C2×C13×C22⋊C8 | C22 | semidirect |
| 20. C2×C13×C22⋊C8 | C22 | semidirect |
| 21. C13×#340 | C22 | semidirect |
| 45. C13×#121 | D4 | semidirect |
| 57. #23925 | C13 | direct (N × H) |
| 103. C2×#535 | C2×C13 | semidirect |
| 104. C2×#447 | C2×C13 | semidirect |
| 105. #1999 | C2×C13 | semidirect |
| 106. #1875 | C2×C13 | semidirect |
| 107. #1780 | C2×C13 | semidirect |
| 146. C23×D4 | C22×C13 | semidirect |
| 152. C2×#121 | C22×C13 | semidirect |
| 155. C2×#117 | C22×C13 | semidirect |
| 157. C2×#102 | C22×C13 | semidirect |
| 158. C2×C22⋊C8 | C22×C13 | semidirect |
| 159. C2×C22⋊C8 | C22×C13 | semidirect |
| 160. #340 | C22×C13 | semidirect |
| 204. #121 | D4×C13 | semidirect |
| 267. C13 | #23925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#535 | 2 |
| C2×C13×#447 | 2 |
| C13×#1999 | 2 |
| C13×#1875 | 2 |
| C13×#1780 | 2 |
| #23925 | 13 |