Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 197 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×#20259311 | C2 | semidirect |
| 3. #27132574 | C2 | semidirect |
| 4. #27132570 | C2 | semidirect |
| 5. #27132542 | C2 | semidirect |
| 6. C4×C22⋊Dic191 | C2 | semidirect |
| 7. C23×Q8×C191 | C2 | semidirect |
| 43. C2×Q8×C191 | D4 | semidirect |
| 81. C22×C191 | #124 | semidirect |
| 101. C191 | #2436 | semidirect |
| 103. C23×Q8 | D191 | semidirect |
| 134. C2×Q8 | C22⋊D191 | semidirect |
| 187. C22 | #20259311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259311 | 2 |
| C2×#20259296 | 2 |
| #27132574 | 2 |
| #27132570 | 2 |
| #27132542 | 2 |
| C4×C22⋊Dic191 | 2 |
| C23×Q8×C191 | 2 |
| #2436 | 191 |