Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
462 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 462 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, socle | C22×C67 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C67 |
| prime radical | C67×#3150 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4×C67 ◁ C2×#97×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#360×C67 | C2 | semidirect |
| 3. C67×#2139 | C2 | semidirect |
| 4. C67×#1944 | C2 | semidirect |
| 5. C67×#1377 | C2 | semidirect |
| 51. #106×C67 | D4 | semidirect |
| 146. #13410 | C67 | direct (N × H) |
| 154. C2×#360 | C2×C67 | semidirect |
| 155. #2139 | C2×C67 | semidirect |
| 156. #1944 | C2×C67 | semidirect |
| 157. #1377 | C2×C67 | semidirect |
| 158. C67 | #13410 | direct (N × H) |
| 204. #106 | D4×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#3150 | 2 |
| C2×#360×C67 | 2 |
| C67×#2139 | 2 |
| C67×#1944 | 2 |
| C67×#1377 | 2 |
| #13410 | 67 |