Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
574 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 98 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C13 |
| prime radical | C13×#2617 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C22⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#1819 | C2 | semidirect |
| 3. C13×#1462 | C2 | semidirect |
| 4. C13×#1344 | C2 | semidirect |
| 5. C13×#1343 | C2 | semidirect |
| 6. C2×C13×#121 | C4 | semidirect |
| 10. C13×#397 | C4 | semidirect |
| 14. C13×#392 | C4 | semidirect |
| 17. C13×#380 | C4 | semidirect |
| 57. #11799 | C13 | direct (N × H) |
| 113. #1819 | C2×C13 | semidirect |
| 114. #1462 | C2×C13 | semidirect |
| 115. #1344 | C2×C13 | semidirect |
| 116. #1343 | C2×C13 | semidirect |
| 179. C2×#121 | C4×C13 | semidirect |
| 183. #397 | C4×C13 | semidirect |
| 187. #392 | C4×C13 | semidirect |
| 190. #380 | C4×C13 | semidirect |
| 334. C13 | #11799 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2617 | 2 |
| C13×#1819 | 2 |
| C13×#1462 | 2 |
| C13×#1344 | 2 |
| C13×#1343 | 2 |
| #11799 | 13 |