Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
454 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #124 |
| commutator, Frattini, cosocle | C2×C42 | C23×C67 |
| socle | C22×C67 | #393 |
| prime radical | #532×C67 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×C42×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C67×#2399 | C2 | semidirect |
| 4. C67×#1303 | C2 | semidirect |
| 5. C67×#1274 | C2 | semidirect |
| 22. C4⋊Q8×C67 | Q8 | semidirect |
| 23. #127×C67 | Q8 | semidirect |
| 135. #10370 | C67 | direct (N × H) |
| 141. #2399 | C2×C67 | semidirect |
| 144. #1303 | C2×C67 | semidirect |
| 145. #1274 | C2×C67 | semidirect |
| 146. C67 | #10370 | direct (N × H) |
| 163. C4⋊Q8 | Q8×C67 | semidirect |
| 164. #127 | Q8×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#2399 | 2 |
| C67×#1963 | 2 |
| C67×#1502 | 2 |
| C67×#1303 | 2 |
| C67×#1274 | 2 |
| #10370 | 67 |