Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
170 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2233 |
| commutator, Frattini, cosocle | C2×C16 | C23×C67 |
| prime radical | C67×#2218 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C2×C4×C67 ◁ C22×C8×C67 ◁ C2×M32×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C67×#2161 | C2 | semidirect |
| 3. C67×#1426 | C2 | semidirect |
| 4. C67×#1419 | C2 | semidirect |
| 5. C67×#1400 | C2 | semidirect |
| 68. #13717 | C67 | direct (N × H) |
| 74. #2161 | C2×C67 | semidirect |
| 75. #1426 | C2×C67 | semidirect |
| 76. #1419 | C2×C67 | semidirect |
| 77. #1400 | C2×C67 | semidirect |
| 78. C67 | #13717 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#2218 | 2 |
| C67×#2161 | 2 |
| C67×#1426 | 2 |
| C67×#1419 | 2 |
| C67×#1400 | 2 |
| #13717 | 67 |