Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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×#20259250 | C2 | semidirect |
| 3. #27132665 | C2 | semidirect |
| 4. #27132664 | C2 | semidirect |
| 5. #27132533 | C2 | semidirect |
| 6. #27132431 | C2 | semidirect |
| 7. C2×#104×C191 | C2 | semidirect |
| 63. C42×C191 | D4 | semidirect |
| 128. C191 | #2039 | semidirect |
| 132. C2×#104 | D191 | semidirect |
| 192. C42 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133241 | 2 |
| C2×#20259250 | 2 |
| #27132665 | 2 |
| #27132664 | 2 |
| #27132533 | 2 |
| #27132431 | 2 |
| C2×#104×C191 | 2 |
| #2039 | 191 |