Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
240 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 50 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 | #327 |
| commutator | C22×C8 | C2×C4×C67 |
| Frattini, cosocle | C2×C4⋊C8 | C22×C67 |
| prime radical | C22×D8×C67 | C4 |
| LCS | G ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4×C67 ◁ C2×C4⋊C8×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C67×#1322 | C2 | semidirect |
| 3. C67×#1290 | C2 | semidirect |
| 96. #7080 | C67 | direct (N × H) |
| 104. #1322 | C2×C67 | semidirect |
| 105. #1290 | C2×C67 | semidirect |
| 106. C67 | #7080 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#2054 | 2 |
| C67×#1322 | 2 |
| C67×#1290 | 2 |
| #7080 | 67 |