Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10587560 | C2 | semidirect |
| 2. #11763185 | C2 | semidirect |
| 3. #11763157 | C2 | semidirect |
| 4. #11763004 | C2 | semidirect |
| 5. #11762942 | C2 | semidirect |
| 6. #11762862 | C2 | semidirect |
| 7. C17×#532 | C2 | semidirect |
| 12. C17×C4⋊Q8 | C22 | semidirect |
| 13. C17×#127 | C22 | semidirect |
| 18. C4×D4×C17 | C22 | semidirect |
| 20. C2×#63228 | C22 | semidirect |
| 26. #10587480 | C22 | semidirect |
| 27. C4⋊#3622 | C22 | semidirect |
| 28. C4×#3622 | C22 | semidirect |
| 74. C2×C4×C17 | D8 | semidirect |
| 107. #532 | D17 | semidirect |
| 125. C4⋊Q8 | C2×D17 | semidirect |
| 130. #127 | C2×D17 | semidirect |
| 135. C4×D4 | C2×D17 | semidirect |
| 141. C17 | #3205 | semidirect |
| 193. C2×C4 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587560 | 2 |
| #11763185 | 2 |
| #11763157 | 2 |
| #11763004 | 2 |
| #11762942 | 2 |
| #11762862 | 2 |
| C17×#532 | 2 |
| #3205 | 17 |