Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
770 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#3213 | C2 | semidirect |
| 2. C13×#3151 | C2 | semidirect |
| 3. C13×#2657 | C2 | semidirect |
| 4. C13×#1555 | C2 | semidirect |
| 5. C13×#1527 | C2 | semidirect |
| 6. C13×#1505 | C2 | semidirect |
| 7. C13×#1300 | C2 | semidirect |
| 44. C13×C4⋊Q8 | D4 | semidirect |
| 50. C13×#127 | D4 | semidirect |
| 67. C13×C4⋊C8 | D4 | semidirect |
| 74. C13×#97 | D4 | semidirect |
| 78. #10088 | C13 | direct (N × H) |
| 134. #3213 | C2×C13 | semidirect |
| 135. #3151 | C2×C13 | semidirect |
| 136. #2657 | C2×C13 | semidirect |
| 137. #1555 | C2×C13 | semidirect |
| 138. #1527 | C2×C13 | semidirect |
| 139. #1505 | C2×C13 | semidirect |
| 140. #1300 | C2×C13 | semidirect |
| 248. C4⋊Q8 | D4×C13 | semidirect |
| 254. #127 | D4×C13 | semidirect |
| 271. C4⋊C8 | D4×C13 | semidirect |
| 278. #97 | D4×C13 | semidirect |
| 344. C13 | #10088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3213 | 2 |
| C13×#3151 | 2 |
| C13×#2657 | 2 |
| C13×#1555 | 2 |
| C13×#1527 | 2 |
| C13×#1505 | 2 |
| C13×#1300 | 2 |
| #10088 | 13 |