Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 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. #22570761 | C2 | semidirect |
| 3. #22570032 | C2 | semidirect |
| 4. #22566154 | C2 | semidirect |
| 5. #22561420 | C2 | semidirect |
| 6. #22561189 | C2 | semidirect |
| 7. #22560421 | C2 | semidirect |
| 8. #22560022 | C2 | semidirect |
| 9. C67×#1965 | C2 | semidirect |
| 134. M16×C67 | #41 | semidirect |
| 206. #1965 | D67 | semidirect |
| 209. C67 | #25690 | semidirect |
| 314. M16 | #11761627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574083 | 2 |
| #22570761 | 2 |
| #22570032 | 2 |
| #22566154 | 2 |
| #22561420 | 2 |
| #22561189 | 2 |
| #22560421 | 2 |
| #22560022 | 2 |
| C67×#1965 | 2 |
| #25690 | 67 |