Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
760 conjugacy classes of subgroups; only the 434 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 434 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #595 |
| commutator, hypocenter | C17 | C22×C4×C8 |
| Frattini | C22 | C23×#595 |
| Fitting | C2×C42×C17 | C4 |
| socle | C23×C17 | C22×C4 |
| prime radical | C23×D17 | C2×C4 |
| cosocle | C2×Dic17 | C24 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#63242 | C2 | direct (N × H) |
| 3. C2×C4×#3624 | C2 | semidirect |
| 8. C2×#63242 | C4 | direct (N × H) |
| 15. C4×#3624 | C22 | semidirect |
| 21. C2×C4×D17 | C8 | semidirect |
| 26. C2×#3624 | C2×C4 | semidirect |
| 28. #63242 | C2×C4 | direct (N × H) |
| 38. C2×C4×C17 | C2×C8 | semidirect |
| 41. C2×Dic17 | C2×C8 | semidirect |
| 47. C4×D17 | C2×C8 | semidirect |
| 49. #3624 | C22×C4 | semidirect |
| 54. C2×D17 | C4×C8 | semidirect |
| 58. C4×C17 | C22×C8 | semidirect |
| 60. Dic17 | C22×C8 | semidirect |
| 66. C2×C17 | C2×C4×C8 | semidirect |
| 69. D17 | C2×C4×C8 | semidirect |
| 81. C17 | C22×C4×C8 | semidirect |
| 111. C2×C4 | #63242 | direct (N × H) |
| 125. C4 | C2×#63242 | direct (N × H) |
| 128. C2 | C4×#63242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63242 | 2 |
| C4×#63242 | 2 |
| C2×C4×#3624 | 2 |
| C2×C42×D17 | 2 |
| C22×C4×C8 | 17 |