Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | C23 |
| commutator | C23 | C22×C4×C17 |
| Frattini, cosocle | C24 | C23×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C17×#95 | C4 | semidirect |
| 52. #1443 | C17 | direct (N × H) |
| 84. #95 | C4×C17 | semidirect |
| 85. C17 | #1443 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#95 | 2 |
| #1443 | 17 |