Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 1. #22575541 | C2 | semidirect |
| 2. #22575540 | C2 | semidirect |
| 3. #22575524 | C2 | semidirect |
| 4. #22575518 | C2 | semidirect |
| 5. #22575517 | C2 | semidirect |
| 6. #22575507 | C2 | semidirect |
| 18. #16864392 | C4 | semidirect |
| 19. #16864391 | C4 | semidirect |
| 20. #16864387 | C4 | semidirect |
| 22. SD16×C269 | C4 | semidirect |
| 51. C269 | #444 | semidirect |
| 64. SD16 | #11761640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575541 | 2 |
| #22575540 | 2 |
| #22575524 | 2 |
| #22575518 | 2 |
| #22575517 | 2 |
| #22575507 | 2 |
| #22575474 | 2 |
| #444 | 269 |