Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×#20259267 | C2 | semidirect |
| 2. #27132904 | C2 | semidirect |
| 4. #27132489 | C2 | semidirect |
| 5. #27132468 | C2 | semidirect |
| 6. #27132465 | C2 | semidirect |
| 7. C2×M32×C191 | C2 | semidirect |
| 39. C16×C191 | D4 | semidirect |
| 75. C191 | #2220 | semidirect |
| 78. C2×M32 | D191 | semidirect |
| 115. C16 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259267 | 2 |
| #27132904 | 2 |
| #27132899 | 2 |
| #27132489 | 2 |
| #27132468 | 2 |
| #27132465 | 2 |
| C2×M32×C191 | 2 |
| #2220 | 191 |