Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
238 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 61 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 | C22×D349 |
| commutator, socle, cosocle | C23×C349 | C23 |
| Fitting | #95×C349 | C2 |
| prime radical | C22×D1396 | C2 |
| hypercenter | #95 | D349 |
| hypocenter | C349 | #394 |
| LCS | G ▷ C23×C349 ▷ C349 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19150212 | C2 | semidirect |
| 3. C2×#19150210 | C2 | semidirect |
| 4. C2×#19150210 | C2 | semidirect |
| 5. #95×C349 | C2 | semidirect |
| 28. C2×Dic349 | D4 | semidirect |
| 57. C349 | #394 | semidirect |
| 63. #95 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1396 | 2 |
| C2×#19150212 | 2 |
| C2×#19150210 | 2 |
| #95×C349 | 2 |
| #394 | 349 |