Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #11763359 | C2 | semidirect |
| 2. #11763122 | C2 | semidirect |
| 3. #11763089 | C2 | semidirect |
| 4. #11763004 | C2 | semidirect |
| 5. #11762943 | C2 | semidirect |
| 6. C4×#63228 | C2 | semidirect |
| 7. #11762862 | C2 | semidirect |
| 8. C2×C4×D4×C17 | C2 | semidirect |
| 23. #10587560 | C22 | semidirect |
| 25. C4×D68 | C22 | semidirect |
| 26. #10587555 | C22 | semidirect |
| 29. #10587480 | C22 | semidirect |
| 30. #10587478 | C22 | semidirect |
| 31. C4⋊#3622 | C22 | semidirect |
| 32. C4×#3622 | C22 | semidirect |
| 73. D4×C17 | #41 | semidirect |
| 80. C2×C4×C17 | D8 | semidirect |
| 116. C2×C4×D4 | D17 | semidirect |
| 153. C17 | #3100 | semidirect |
| 199. D4 | #63252 | semidirect |
| 208. C2×C4 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| #11763122 | 2 |
| #11763089 | 2 |
| #11763004 | 2 |
| #11762943 | 2 |
| C4×#63228 | 2 |
| #11762862 | 2 |
| C2×C4×D4×C17 | 2 |
| #3100 | 17 |