Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763214 | C2 | semidirect |
| 3. #11763149 | C2 | semidirect |
| 4. #11763094 | C2 | semidirect |
| 5. #11763047 | C2 | semidirect |
| 7. #11762846 | C2 | semidirect |
| 8. C4×Q16×C17 | C2 | semidirect |
| 84. C4×Q16 | D17 | semidirect |
| 110. C17 | #3342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763532 | 2 |
| #11763214 | 2 |
| #11763149 | 2 |
| #11763094 | 2 |
| #11763047 | 2 |
| C8×D68 | 2 |
| #11762846 | 2 |
| C4×Q16×C17 | 2 |
| #3342 | 17 |