Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763460 | C2 | semidirect |
| 2. #11763213 | C2 | semidirect |
| 3. #11763124 | C2 | semidirect |
| 4. #11763122 | C2 | semidirect |
| 5. #11763088 | C2 | semidirect |
| 6. #11763046 | C2 | semidirect |
| 7. #11763045 | C2 | semidirect |
| 8. #11762891 | C2 | semidirect |
| 9. C8×C22⋊D17 | C2 | semidirect |
| 10. #107×D17 | C2 | semidirect |
| 11. C2×C17×#107 | C2 | semidirect |
| 81. C22⋊D17 | D8 | semidirect |
| 95. C8×C17 | #41 | semidirect |
| 128. C2×#107 | D17 | semidirect |
| 162. C17 | #3334 | semidirect |
| 221. C8 | #63252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763460 | 2 |
| #11763213 | 2 |
| #11763124 | 2 |
| #11763122 | 2 |
| #11763088 | 2 |
| #11763046 | 2 |
| #11763045 | 2 |
| #11762891 | 2 |
| C8×C22⋊D17 | 2 |
| #107×D17 | 2 |
| C2×C17×#107 | 2 |
| #3334 | 17 |