Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1174 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 106 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 | C23×C4 | C23×C13 |
| LCS | G ▷ C23×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 |
|---|---|---|
| 1. C13×#3192 | C2 | semidirect |
| 2. C13×#2433 | C2 | semidirect |
| 3. C13×#1783 | C2 | semidirect |
| 4. C13×#1507 | C2 | semidirect |
| 5. C13×#1297 | C2 | semidirect |
| 28. C22×D4×C13 | D4 | semidirect |
| 32. C2×C13×M16 | D4 | semidirect |
| 39. C2×C13×C4⋊C4 | D4 | semidirect |
| 49. C13×#95 | D4 | semidirect |
| 50. #10326 | C13 | direct (N × H) |
| 94. #3192 | C2×C13 | semidirect |
| 95. #2433 | C2×C13 | semidirect |
| 96. #1783 | C2×C13 | semidirect |
| 97. #1507 | C2×C13 | semidirect |
| 98. #1297 | C2×C13 | semidirect |
| 182. C22×D4 | D4×C13 | semidirect |
| 186. C2×M16 | D4×C13 | semidirect |
| 193. C2×C4⋊C4 | D4×C13 | semidirect |
| 203. #95 | D4×C13 | semidirect |
| 253. C13 | #10326 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3192 | 2 |
| C13×#2433 | 2 |
| C13×#1783 | 2 |
| C13×#1507 | 2 |
| C13×#1297 | 2 |
| #10326 | 13 |