Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1034 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #386 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C13×#2433 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#2308 | C2 | semidirect |
| 3. C13×#1783 | C2 | semidirect |
| 4. C13×#1510 | C2 | semidirect |
| 5. C13×#1284 | C2 | semidirect |
| 7. C2×C13×#127 | C4 | semidirect |
| 15. C13×#390 | C4 | semidirect |
| 30. C22×D4×C13 | C2×C4 | semidirect |
| 40. C2×C13×C4⋊C4 | C2×C4 | semidirect |
| 50. C2×C42×C13 | C2×C4 | semidirect |
| 56. C13×#95 | D4 | semidirect |
| 57. #9463 | C13 | direct (N × H) |
| 117. #2308 | C2×C13 | semidirect |
| 118. #1783 | C2×C13 | semidirect |
| 119. #1510 | C2×C13 | semidirect |
| 120. #1284 | C2×C13 | semidirect |
| 182. C2×#127 | C4×C13 | semidirect |
| 190. #390 | C4×C13 | semidirect |
| 241. C22×D4 | C2×C4×C13 | semidirect |
| 251. C2×C4⋊C4 | C2×C4×C13 | semidirect |
| 261. C2×C42 | C2×C4×C13 | semidirect |
| 267. #95 | D4×C13 | semidirect |
| 335. C13 | #9463 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2433 | 2 |
| C13×#2308 | 2 |
| C13×#1783 | 2 |
| C13×#1510 | 2 |
| C13×#1284 | 2 |
| #9463 | 13 |