Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
372 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 88 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. #22626291 | C2 | semidirect |
| 2. #22625489 | C2 | semidirect |
| 3. #22624887 | C2 | semidirect |
| 4. #22624886 | C2 | semidirect |
| 71. D584 | M16 | semidirect |
| 89. Q16×C73 | M16 | semidirect |
| 156. C73 | #11660 | semidirect |
| 219. Q16 | #11924038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626291 | 2 |
| #22625489 | 2 |
| #22624887 | 2 |
| #22624886 | 2 |
| C4×#14556614 | 2 |
| #11660 | 73 |