Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#10587593 | C2 | semidirect |
| 2. C22×#63218 | C2 | semidirect |
| 4. #11762886 | C2 | semidirect |
| 5. #11762879 | C2 | semidirect |
| 6. #11762775 | C2 | semidirect |
| 7. #11762772 | C2 | semidirect |
| 8. #11762765 | C2 | semidirect |
| 9. C17×#424 | C2 | semidirect |
| 21. C2×#63218 | C22 | semidirect |
| 22. C2×C8×D17 | C22 | semidirect |
| 28. C17×C4⋊C8 | C22 | semidirect |
| 30. #10587491 | C22 | semidirect |
| 31. #10587474 | C22 | semidirect |
| 32. C4×#3622 | C22 | semidirect |
| 58. C2×#3622 | D4 | semidirect |
| 114. #424 | D17 | semidirect |
| 141. C4⋊C8 | C2×D17 | semidirect |
| 146. C17 | #2930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587593 | 2 |
| C22×#63218 | 2 |
| #11763321 | 2 |
| #11762886 | 2 |
| #11762879 | 2 |
| #11762775 | 2 |
| #11762772 | 2 |
| #11762765 | 2 |
| C17×#424 | 2 |
| #2930 | 17 |