Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
952 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D191 |
| commutator, socle, cosocle | C23×C191 | C24 |
| Fitting | C22×#41×C191 | C2 |
| hypercenter | C22×#41 | D191 |
| hypocenter | C191 | #2431 |
| LCS | G ▷ C23×C191 ▷ C191 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20259318 | C2 | semidirect |
| 2. C2×#20259311 | C2 | semidirect |
| 3. C2×#20259296 | C2 | semidirect |
| 4. #27132571 | C2 | semidirect |
| 5. #27132570 | C2 | semidirect |
| 6. #27132566 | C2 | semidirect |
| 7. #27132542 | C2 | semidirect |
| 8. C4×C22⋊Dic191 | C2 | semidirect |
| 9. C22×#41×C191 | C2 | semidirect |
| 57. C2×Q8×C191 | D4 | semidirect |
| 63. C2×D4×C191 | D4 | semidirect |
| 69. C22×C4×C191 | D4 | semidirect |
| 88. C2×Dic191 | #41 | semidirect |
| 148. C191 | #2431 | semidirect |
| 150. C22×#41 | D191 | semidirect |
| 188. C2×Q8 | C22⋊D191 | semidirect |
| 202. C2×D4 | C22⋊D191 | semidirect |
| 211. C22×C4 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259318 | 2 |
| C2×#20259311 | 2 |
| C2×#20259296 | 2 |
| #27132571 | 2 |
| #27132570 | 2 |
| #27132566 | 2 |
| #27132542 | 2 |
| C4×C22⋊Dic191 | 2 |
| C22×#41×C191 | 2 |
| #2431 | 191 |