Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
364 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 179 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. #11762939 | C2 | semidirect |
| 3. #11762936 | C2 | semidirect |
| 4. Q8×#3622 | C2 | semidirect |
| 7. C8×Q8×C17 | C2 | semidirect |
| 74. C8×Q8 | D17 | semidirect |
| 97. C17 | #2984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D17 | 2 |
| #11762939 | 2 |
| #11762936 | 2 |
| Q8×#3622 | 2 |
| #11762865 | 2 |
| #11762860 | 2 |
| C8×Q8×C17 | 2 |
| #2984 | 17 |