Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23752616 | C2 | semidirect |
| 3. #23752590 | C2 | semidirect |
| 4. #23752561 | C2 | semidirect |
| 8. C4×Dic604 | C2 | semidirect |
| 9. C4×#14558994 | C2 | semidirect |
| 11. C4×Q16×C151 | C2 | semidirect |
| 83. C4×D151 | Q16 | semidirect |
| 114. C151 | #3170 | semidirect |
| 125. C4×Q16 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752766 | 2 |
| #23752616 | 2 |
| #23752590 | 2 |
| #23752561 | 2 |
| #23752454 | 2 |
| #23752452 | 2 |
| #23752450 | 2 |
| C4×Dic604 | 2 |
| C4×#14558994 | 2 |
| C4×C8×D151 | 2 |
| C4×Q16×C151 | 2 |
| #3170 | 151 |