Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
182 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11762888 | C2 | semidirect |
| 3. #11762561 | C2 | semidirect |
| 4. D4⋊#3622 | C2 | semidirect |
| 5. #11762536 | C2 | semidirect |
| 6. #11762530 | C2 | semidirect |
| 7. C8×D4×C17 | C2 | semidirect |
| 45. D4×C17 | M16 | semidirect |
| 59. C8×C17 | D8 | semidirect |
| 81. C8×D4 | D17 | semidirect |
| 106. C17 | #1581 | semidirect |
| 131. D4 | #63218 | semidirect |
| 147. C8 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63228 | 2 |
| #11762888 | 2 |
| #11762561 | 2 |
| D4⋊#3622 | 2 |
| #11762536 | 2 |
| #11762530 | 2 |
| C8×D4×C17 | 2 |
| #1581 | 17 |