Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
4086 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 4086 conjugacy classes of subgroups — too many to draw. Only its 811 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D13 |
| commutator, socle, cosocle | C23×C13 | C25 |
| Fitting | C13×#2867 | C2 |
| hypercenter | #2867 | D13 |
| hypocenter | C13 | #36644 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #2867 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11719421 | C2 | semidirect |
| 2. #13123234 | C2 | semidirect |
| 3. #13123192 | C2 | semidirect |
| 4. #13123178 | C2 | semidirect |
| 5. #127×Dic13 | C2 | semidirect |
| 6. C43×D13 | C2 | semidirect |
| 7. C13×#2867 | C2 | semidirect |
| 44. C42×D13 | D4 | semidirect |
| 65. C42×C13 | #41 | semidirect |
| 73. #2867 | D13 | semidirect |
| 95. C4×D13 | #127 | semidirect |
| 119. C4×C13 | #532 | semidirect |
| 173. C42 | #6129 | semidirect |
| 174. C13 | #36644 | semidirect |
| 204. C4 | #11719421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719421 | 2 |
| #13123234 | 2 |
| #13123192 | 2 |
| #13123178 | 2 |
| #127×Dic13 | 2 |
| C43×D13 | 2 |
| C13×#2867 | 2 |
| #36644 | 13 |