Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
3464 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 354 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊#595 | C2 | semidirect |
| 2. #11763750 | C2 | direct (N × H) |
| 4. C25×C17 | C4 | semidirect |
| 6. C24×D17 | C4 | semidirect |
| 7. C24×D17 | C4 | semidirect |
| 10. C23×#595 | C22 | semidirect |
| 12. C2×C22⋊#595 | C22 | semidirect |
| 15. C24×C17 | C2×C4 | semidirect |
| 24. C23×D17 | C2×C4 | semidirect |
| 29. C22×#595 | C23 | semidirect |
| 34. C23×C17 | C22⋊C4 | semidirect |
| 46. C22×D17 | C22⋊C4 | semidirect |
| 47. C22×D17 | C22⋊C4 | semidirect |
| 60. C22×C17 | C2×C22⋊C4 | semidirect |
| 68. C2×D17 | C2×C22⋊C4 | semidirect |
| 76. C2×C17 | #379 | semidirect |
| 79. D17 | #379 | semidirect |
| 86. C25 | #595 | semidirect |
| 90. C17 | C2×#379 | semidirect |
| 105. C24 | C2×#595 | semidirect |
| 128. C23 | C22⋊#595 | semidirect |
| 146. C22 | C2×C22⋊#595 | semidirect |
| 153. C2 | #11763750 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#595 | 2 |
| #11763750 | 2 |
| C25×D17 | 2 |
| C2×#379 | 17 |