Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #11762860 | C2 | semidirect |
| 3. #11762831 | C2 | semidirect |
| 4. #11762538 | C2 | semidirect |
| 5. D4⋊#3622 | C2 | semidirect |
| 6. #11762536 | C2 | semidirect |
| 7. C17×D4⋊C8 | C2 | semidirect |
| 20. C17×C4⋊C8 | C22 | semidirect |
| 21. C4×C8×C17 | C22 | semidirect |
| 25. C4⋊#3622 | C22 | semidirect |
| 26. C4×#3622 | C22 | semidirect |
| 66. D4×C17 | M16 | semidirect |
| 80. D68 | M16 | semidirect |
| 122. D4⋊C8 | D17 | semidirect |
| 144. C4⋊C8 | C2×D17 | semidirect |
| 147. C4×C8 | C2×D17 | semidirect |
| 148. C17 | #1486 | semidirect |
| 191. D4 | #63218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D17 | 2 |
| #11762860 | 2 |
| #11762831 | 2 |
| #11762538 | 2 |
| D4⋊#3622 | 2 |
| #11762536 | 2 |
| C17×D4⋊C8 | 2 |
| #1486 | 17 |