Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
828 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 154 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 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#459 | C2 | semidirect |
| 2. C13×#2537 | C2 | semidirect |
| 3. C13×#1957 | C2 | semidirect |
| 4. C2×C13×D4⋊C8 | C2 | semidirect |
| 5. C13×#1296 | C2 | semidirect |
| 32. C13×#127 | D4 | semidirect |
| 46. C13×C4⋊C8 | D4 | semidirect |
| 51. #10228 | C13 | direct (N × H) |
| 71. C2×D4×C13 | D8 | semidirect |
| 100. C2×#459 | C2×C13 | semidirect |
| 101. #2537 | C2×C13 | semidirect |
| 102. #1957 | C2×C13 | semidirect |
| 103. C2×D4⋊C8 | C2×C13 | semidirect |
| 104. #1296 | C2×C13 | semidirect |
| 201. #127 | D4×C13 | semidirect |
| 215. C4⋊C8 | D4×C13 | semidirect |
| 246. C2×D4 | C13×D8 | semidirect |
| 275. C13 | #10228 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#459 | 2 |
| C13×#2537 | 2 |
| C13×#1957 | 2 |
| C2×C13×D4⋊C8 | 2 |
| C13×#1296 | 2 |
| #10228 | 13 |