Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11763532 | C2 | semidirect |
| 3. #11763155 | C2 | semidirect |
| 4. #11763131 | C2 | semidirect |
| 5. #11763090 | C2 | semidirect |
| 6. #11763052 | C2 | semidirect |
| 7. #11762958 | C2 | semidirect |
| 8. C4×#63230 | C2 | semidirect |
| 9. #11762886 | C2 | semidirect |
| 10. #11762812 | C2 | semidirect |
| 11. C17×#460 | C2 | semidirect |
| 14. C2×SD16×C17 | C22 | semidirect |
| 16. C4×Q8×C17 | C22 | semidirect |
| 17. #10587632 | C22 | semidirect |
| 22. C2×#63218 | C22 | semidirect |
| 24. #10587578 | C22 | semidirect |
| 28. #10587555 | C22 | semidirect |
| 30. C17×C4⋊C8 | C22 | semidirect |
| 31. C17×#102 | C22 | semidirect |
| 32. #10587506 | C22 | semidirect |
| 33. #10587503 | C22 | semidirect |
| 34. #10587503 | C22 | semidirect |
| 36. #10587491 | C22 | semidirect |
| 37. #10587489 | C22 | semidirect |
| 39. #10587479 | C22 | semidirect |
| 40. C4×#3622 | C22 | semidirect |
| 136. #460 | D17 | semidirect |
| 150. C2×SD16 | C2×D17 | semidirect |
| 161. C4×Q8 | C2×D17 | semidirect |
| 167. C4⋊C8 | C2×D17 | semidirect |
| 173. #102 | C2×D17 | semidirect |
| 176. C17 | #3324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763532 | 2 |
| #11763444 | 2 |
| #11763155 | 2 |
| #11763131 | 2 |
| #11763090 | 2 |
| #11763052 | 2 |
| #11762958 | 2 |
| C4×#63230 | 2 |
| #11762886 | 2 |
| #11762812 | 2 |
| C17×#460 | 2 |
| #3324 | 17 |