Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#20259255 | C2 | semidirect |
| 4. C2×#20259232 | C2 | semidirect |
| 5. #27132570 | C2 | semidirect |
| 7. C2×#103×C191 | C2 | semidirect |
| 11. C2×#15690274 | C4 | semidirect |
| 70. C191⋊C8 | C22⋊C4 | semidirect |
| 112. C191 | #1973 | semidirect |
| 116. C2×#103 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690274 | 2 |
| C2×#20259255 | 2 |
| C2×#20259244 | 2 |
| C2×#20259232 | 2 |
| #27132570 | 2 |
| #27132564 | 2 |
| C2×#103×C191 | 2 |
| #1973 | 191 |