Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
750 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 750 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×C67 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C67 |
| prime radical | C67×#3192 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#448×C67 | C2 | semidirect |
| 3. C67×#1784 | C2 | semidirect |
| 4. C67×#1471 | C2 | semidirect |
| 5. C67×#1298 | C2 | semidirect |
| 135. #9988 | C67 | direct (N × H) |
| 142. C2×#448 | C2×C67 | semidirect |
| 143. #1784 | C2×C67 | semidirect |
| 144. #1471 | C2×C67 | semidirect |
| 145. #1298 | C2×C67 | semidirect |
| 146. C67 | #9988 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#3192 | 2 |
| C2×#448×C67 | 2 |
| C67×#1784 | 2 |
| C67×#1471 | 2 |
| C67×#1298 | 2 |
| #9988 | 67 |