Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
590 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 214 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C24×C13 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#2236 | C2 | semidirect |
| 3. C13×#2216 | C2 | semidirect |
| 4. C13×#2188 | C2 | semidirect |
| 9. C2×C13×Q32 | C22 | semidirect |
| 17. C13×#366 | C22 | semidirect |
| 18. C13×#358 | C22 | semidirect |
| 44. #33755 | C13 | direct (N × H) |
| 75. #2236 | C2×C13 | semidirect |
| 76. #2216 | C2×C13 | semidirect |
| 77. #2188 | C2×C13 | semidirect |
| 81. C23×C13 | Q32 | semidirect |
| 106. C2×Q32 | C22×C13 | semidirect |
| 114. #366 | C22×C13 | semidirect |
| 115. #358 | C22×C13 | semidirect |
| 189. C13 | #33755 | direct (N × H) |
| 192. C23 | C13×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#467 | 2 |
| C13×#2236 | 2 |
| C13×#2216 | 2 |
| C13×#2188 | 2 |
| C2×C13×C22⋊C16 | 2 |
| #33755 | 13 |