Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
208 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | D4 |
| commutator | C4 | C4×C8×C17 |
| Frattini, cosocle | C2×C42 | C22×C17 |
| socle, prime radical | C23×C17 | C22⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C17×C4⋊C8 | C4 | semidirect |
| 12. C4×C8×C17 | C4 | semidirect |
| 24. C4⋊C4×C17 | C8 | semidirect |
| 50. #1279 | C17 | direct (N × H) |
| 80. C4⋊C8 | C4×C17 | semidirect |
| 82. C4×C8 | C4×C17 | semidirect |
| 84. C17 | #1279 | direct (N × H) |
| 95. C4⋊C4 | C8×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×C4⋊C8 | 2 |
| C2×C4×C8×C17 | 2 |
| C4×C4⋊C4×C17 | 2 |
| #1279 | 17 |