Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
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. #22551680 | C2 | semidirect |
| 2. #22551679 | C2 | semidirect |
| 3. #22551663 | C2 | semidirect |
| 4. #22551657 | C2 | semidirect |
| 5. #22551656 | C2 | semidirect |
| 6. #22551646 | C2 | semidirect |
| 18. #16861608 | C4 | semidirect |
| 19. #16861607 | C4 | semidirect |
| 20. #16861603 | C4 | semidirect |
| 22. SD16×C257 | C4 | semidirect |
| 51. C257 | #444 | semidirect |
| 64. SD16 | #11759967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551680 | 2 |
| #22551679 | 2 |
| #22551663 | 2 |
| #22551657 | 2 |
| #22551656 | 2 |
| #22551646 | 2 |
| #22551613 | 2 |
| #444 | 257 |